**Discrete Wavelet Transform Based Differential Protection for Power Transformers**

**Transformers are a critical and expensive equipment in the power system network. They function as a node to connect two different voltage levels. Hence, the availability of their service is vital in maintaining the continuous power supply to consumers. Since many decades, differential protection provides the best overall protection for a power transformer to protect against faults... **

* * **- Narri Yadaiah, Nagireddy Ravi**

In this article a wavelet transform based differential protection scheme for three phase power transformers has been presented. The proposed technique uses wavelet transforms for characterization of different transients, which will aid in the development of a novel differential protection scheme for power transformers.

The results of wavelet based differential protection reveal for identification of inrush currents and distinguish from other type of faults – such as internal and external short circuit faults.

The functioning of power transformer is crucial to maintain uninterrupted supply to the consumers. Hence proper detection of fault helps in isolation of the defective transformer, and thereby avoiding unnecessary outages and instability of the power system – and ensures good power quality. To accomplish these objectives, an efficient fault detection method will help the electric utilities enhance the availability of generation and T&D.

**Differential Protection**

Traditionally, differential protection for power transformers has been used for decades. The principle of differential protection scheme is one simple technique. The differential relay compares the primary current and secondary current of power transformer, the differential current due to disbalance found in primary and secondary currents will actuate the relay to trip the breaker, thereby isolate the faulty system. The schematic diagram of differential protection for power transformer is shown in Fig. 1.**Fig. 1: Connection diagram of differential protection for power transformer...****Discrete Wavelet transform (DWT)**

The Wavelet Transform has been introduced in place of Fourier analysis and received considerable interest in fields such as acoustics, voice communications and seismic etc. – and this technique is a powerful mathematical tool for signal analysis and can be used for wide range of applications such as signal processing, data compression, speech recognition, wave propagation and pattern recognition. In recent study, wavelet transform has been implemented for fault detection in power system equipment that use wavelet transforms – and this technique is efficient in fault detection of power system components. Wavelet transform has a special feature, which translates the time-amplitude representation of a signal to time-frequency representation – that is encapsulated as a set of wavelet coefficients. The wavelet transforms can be analysed using Continuous Wavelet Transforms (CWT) and Discrete Wavelet Transforms (DWT).

In this article a discrete wavelet transform is used for fault detection – because of improved resolution, less computational time and memory required to calculate the wavelet coefficients. The DWT is defined as follows:

where a0 and b0 are fixed constants with a_{0} > 1, b_{0} > 1 and m, n are positive integer variables. The values of a_{0} and b_{0} are elected such that mother wavelets form an orthonormal basis. The orthonormal basis satisfies if a_{0} = 2 and b_{0} =1.

The implementation of the DWT with a filter bank is effective for analysing the information of the signals. The DWT is computed by analysing the signal at different frequency bands with different resolutions by decomposing the signal into coarse approxi- mation and detailed information. Using this technique any wavelet such as Haar, Daubechies, Symlets Coiflets and Bior 4.4 etc., can be implemented.

The selection of mother wavelet is an important role as it enhances the performance of fault detection scheme, and the process leads to an accurate fault classification thereby protecting transformer from faults. In order to select the most capable mother wavelet, different mother wavelets such as Haar, Daubechies, Symlets, Coiflets and Bior 4.4 wavelet have been considered and compared. Bior 4.4 is simply chosen since it gives a more accurate result in detecting low amplitude, short duration, fast decaying transients and minimum error during the magnetizing inrush condition.

**Proposed diff.protection scheme using DWT**

The DWT technique has been proposed for differential protection of power transformers. The wavelet decomposition technique analyses the transient signal which characterises the condition of the component. The primary current and secondary currents of power transformer are measured through Current Transformers (CTs) are used for signal analysis such as normal operation, magnetising inrush and short circuit faults.

Wavelet technique, a time-scale domain approach is applied to detect the magnetizing inrush and short circuit faults by comparing with normal operation of power transformer. The signal obtained from the CTs of power transformer is passed through a low pass and a high pass filter to obtain approximate coefficients and detail coefficients respectively. The structure of the proposed DWT based differential protection scheme used for detecting faults and classifying different transients is shown in Fig. 2. The fault detection is summarised as below step by step

**Step 1:**Obtain the primary current and secondary current signals from the terminals of Current Transformers (CTs)**Step 2:**Apply DWT for the current signals obtained in step 1 and calculation of differential current**Step 3:**Identify the fault through interpretation of detailed wavelet coefficients of differential current**Step 4:**Distinguish between a magnetising current, internal short circuit current, external short circuit current and normal operation current.

**Fig. 2: Structure of proposed differential protection scheme...**

Simulation, Results and Discussions

A power system network, with a three phase transformer and a load, is shown in Figure 3. is simulated using MATLAB/SIMULINK software. Table 1 presents the parameters associated with the power transformer.**Fig. 3: Single line diagram for the simulation model...**

The power transformer is simulated for various types of transients. The primary and secondary currents are measured and the discrete wavelet analysis is performed on signals obtained. The simulation is carried out for 0.2 sec and the data is captured for 10-cycles.**Normal Operation**

**Fig. 4(a): Normal current entering at primary side...****Fig. 4(b): Normal current leaving the secondary side...**

**Fig. 4(c): DWT of normal current at primary side...**

**Fig. 4(d): DWT of normal current at secondary side...**

**Fig. 4(e): DWT of differential normal current...**

The output currents from both primary and secondary side CTs are analysed for comparison with other conditions like internal and external faults in the system. During normal operation, there is no malfunctioning of the transformer – and hence the wavelet decomposed output signal is a straight line. The current signal obtained from the CTs of power transformer and DWT analysis for normal operating condition are as shown in Fig. 4 (a) to 4 (e).

**Magnetising Inrush**

When a power transformer is energised, it generates inrush current, the magnitude of this current will be 1 to 2 % of rated current. This type of transient may cause unnecessary tripping of transformer. In time domain signal analysis, it can be observed spikes during the entire in rush transient period whereas in DWT localsation can be observed in 600th sample which corresponds to 0.12 sec, which is the time of enerziation of power transformer. The current signal obtained from the CTs of power transformer and DWT analysis for magnetising inrush condition are as shown in Fig 5 (a) to 5 (e). The DWT coefficients are lower compared to other transients such as magnetising inrush current and external fault which enables the restrain relay to operate.** Fig. 5(a): Inrush current entering at primary side...****Fig. 5(b): Inrush current leaving the secondary side...****Fig. 5(c): DWT of inrush current at primary side...****Fig. 5(d): DWT of inrush current at secondary side...****Fig. 5(e): DWT of differential inrush currents...**

**Internal Fault**

Short circuits in transformers results in currents of high magnitude. The detection of short circuit fault is essential – and requires fast action by protective relay to de-energize transformer, otherwise this leads to extreme mechanical stress of core and coil assembly. The simulation was carried out for 0.2 sec. The short circuit fault is set to occur at instants 0.12 sec and cleared at 0.14 sec that is the total fault time is 0.02 sec. The peak primary current is measured for an internal short circuit fault is 1000 A. The spikes can be observed at the short circuit time and there is a differential current and DWT coefficients are high compared to other transients such as magnetising inrush current and external fault, which enable the relay to operate. The current signal obtained from the CTs of power transformer and DWT analysis for internal fault are as shown in Fig. 6 (a) to 6 (e).**Fig. 6(a): Internal fault current entering at primary side...****Fig. 6(b): Internal fault current leaving the secondary side...****Fig. 6(c): DWT of internal fault current at primary side...****Fig. 6(d): DWT of internal fault current at secondary side...****Fig. 6(e): DWT of differential internal fault current...**

**External Fault**

External faults are system faults that occur outside the transformer differential protection zone. The external fault event also appears to be localised and DWT coefficients at fault time are higher than their values beyond or before this time. The fault existence timing is 0.12 sec to 0.14 sec. The fault selected for analysis is LL-G fault. The current signal obtained from the CTs of power transformer and DWT analysis for external fault are as shown in Fig 7 (a) to 7 (e). The DWT coefficients are lower compared to internal fault, hence DWT based relay performs correctly and remains stable as the conventional scheme does.**Fig. 7(a): External fault current entering at primary side...**

**Fig. 7(b): External fault current leaving the secondary side... ****Fig. 7(c): DWT of external fault current at primary side... ****Fig. 7(d): DWT of external fault current at secondary side... ****Fig. 7(e): DWT of differential external fault current...** **Conclusions**

This article presented a new scheme based on discrete wavelet transform differential protection of power transformer. The wavelet decomposition breaks up signal into both time and frequency, allowing for a complete and efficient description of signal. This information is very important in detecting the fault. It is observed from the coefficients that fault is seen to be localised.

The wavelet transform is applied to normal operation, magnetising inrush currents, internal fault condition and external fault condition. It is also concluded from the obtained results that this technique is better in characterisation and discrimination of faults.

Application of wavelet transforms for differential protection scheme of transformer protection enhances the drawbacks arising in conventional differential protection method as fault localisation and characterisation is very precise.

**Authors are from JNTUH College of Engineering, Kukatpally, Hyderabad and Telangana State Power Generation Corporation Ltd, Telangana. **