**2. Conventional differential protection scheme**

This scheme is based on the principle that the input power to the power transformer under normal conditions is equal to the output power. Under normal conditions, no current will flow into the differential relay current coil. Whenever a fault occurs, within the protected zone, the current balance will no longer exist, and relay contacts will close and release a trip signal to cause the certain circuit breakers (CBs) to operate in order to disconnect the faulty equipment/part. The differential relay compares the primary and secondary side currents of the power transformer. Current transformers (CTs) are used to reduce the amount of currents in such a way their secondary side currents are equal. Fig. 1 shows the differential relay in its simplest form. The polarity of CTs is such as to make the current circulate normally without going through the relay, during normal load conditions and external faults.

Current transformers ratings are selected carefully to be matched with the power transformer current ratings to which they are connected so as the CTs secondary side currents are equal. However, the problem is that the CTs ratios available in the market have standard ratings. They are not available exactly as the desired ratings. Therefore, the

© 2012 Aktaibi and Rahman, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Aktaibi and Rahman, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

$$I\_1 = \frac{l\_p}{N\_1} \tag{1}$$

$$I\_2 = \frac{l\_s}{N\_2} \tag{2}$$

$$I\_d = \frac{I\_p}{N\_1} - \frac{I\_s}{N\_2} \tag{3}$$

$$\frac{I\_p}{I\_s} = \frac{N\_s}{N\_p} \tag{4}$$

$$I\_s = \frac{I\_p \times N\_p}{n\_s} \tag{5}$$

$$I\_d = \frac{I\_p}{N\_1} - \frac{I\_p \times \left(N\_p / N\_s\right)}{N\_2}$$

$$I\_d = \frac{I\_p}{N\_1} \left(1 - \frac{N\_p / N\_s}{N\_2 / N\_1}\right) \tag{6}$$

$$\lambda = \left(1 - \frac{N\_p / N\_s}{N\_2 / N\_1}\right)$$

From equation (6) it is obvious that the term � must be equal to zero in order to make �� = 0

$$(1 - \frac{N\_p/N\_s}{N\_2/N\_1}) = 0$$

$$\frac{N\_2}{N\_1} = \frac{N\_p}{N\_s} \tag{7}$$

Equation (7) gives the condition for the security of the differential relay, which means the reciprocal of the ratio of the secondary side turns of the CTs must equal to the turns ratio of the power transformer.

In power transformers, the input power is equal to the output power. However, the voltage and the current in both the primary and secondary sides are different depending on whether the transformer is step up or step down. For instance, if the transformer is step up that means; the input voltage of the power transformer is low and the current is high, meantime the voltage in the secondary side is high and the current is low. This action makes both the input and output power equal. Due to this nature the CTs in the primary and the secondary sides of the power transformer do not have same turn ratio. However, they are carefully selected, in terms of turn ratio and magnetizing characteristics, so that they have the same output current at normal conditions of operations. If identical CTs are not available, the closer ones are chosen and then the mismatch between them is compensated by using the interposing CTs. The interposing CTs can fix the mismatch in the CTs; however they add their own burden to the output of the main CTs.

The same argument is applied for three phase �3�) transformers, except some extra issues may appear in polyphase transformers. Figure 4 shows the schematic diagram of the 3� differential protection.

In some cases, of 3� power transformer connections as shown in figure 5, a 30� phase shift between primary and secondary currents is taking place. This phase shift occurs in the Y or -Y connected transformers due to the transformation of the current from Y- or -Y as illustrated in the figure 4. This phase shift can be corrected easily by connecting the CTs secondary circuits in opposite way to the way that the power transformer phases are connected. I.e. if the transformer windings are connected in Y- the CTs secondary windings should be connected in -Y and vice versa [20]. As shown in figure 4 the relation between the line-to-line voltage ����) to the phase voltage (���) can explain the phase shift between the -Y transformer connection. The following equation gives the relationship between the line-to-line voltage ����) to the phase voltage (���) [2], [3], [6], [7]:
