Question

Question:Select such that the differential relay characteristic shown in Figure 10.34 blocks for up to 20% mismatch between I₁ and I₂ .

Short answer

Answer

The value of k is 0.1818 .

Step-by-step solution

Write the given data from the question.

Consider the20% mismatch between I₁ and I₂ .

Determine the formula of slope of the graph showing trip and block regions of the relay.

Write the formula ofslope of the graph showing trip and block regions of the relay as .

$\frac{\mathbf{2}+\mathbf{k}}{\mathbf{2}-\mathbf{k}}=\mathbf{1}\mathbf{.}\mathbf{2}$ …… (1)

Here, k is a differential relay characteristic.

 Determine the value of  k.

Draw a graph showing the various regions of differential relays (trip and block):

From Figure 1, assume the slope of the graph showing trip and block regions of the relay as .

Determine the value of .

Solve equation (1) and find the value of .

Solve further as,

$$\begin{gathered} 2+k=\left(1.2\right)\left(2-k\right) \\ 2+k=2.4-1.2k \\ k+1.2k=2.4-2 \\ k=\frac{0.4}{2.2} \end{gathered}$$

k=0.1818

Therefore, the value of k is 0.1818 .