Question

The relay in Problem 10.2 has a time-dial setting of 4. Determine the relay operating time if the primary fault current is 400 A.

Short answer

The relay operating time is 3.6 sec.

Step-by-step solution

write the given data from the question.

The CT ratio n = 100 : 5.

Current tap setting TS = 5 A.

Primary fault current I = 400 A.

Determine the formula to calculate the relay operating time.

The equation to calculate the secondary voltage of the CT is given as follows.

E' = I' (Z' + Z_B) …… (1)

Here I'is the relay current, and Z_B is the relay impedance.

The equation to calculate the minimum primary fault current is given as follows.

I = n ( I' + I_c) …… (2)

Here, I_c is the exciting current.

Calculate the relay operating time.

Consider the CT equivalent circuit as,

Refer to the excitation curve for CO-8 relay in the text book.

The relay current, I' = 10 A

Relay impedance,$Z_B=1\Omega$

Calculate the secondary voltage of the CT,

Substitute 10 A for I', $0.082\Omega$for Z' and $1\Omega$ for Z_B into equation (1).

$$\begin{gathered} E\text{'}=10(0.082+1) \\ E\text{'}=10\times 1.082 \\ E\text{'}=10.82V \end{gathered}$$

The exciting current corresponding to the secondary voltage of the CT 10.82 V is 0.6 A.

I_c = 0.6 A

Calculate the minimum primary fault current.

Substitute 100 : 5 for n, 10 A for I' and 0.6 A for I_c into equation (2).

$$\begin{gathered} I=\frac{100}{5}(10+0.6) \\ I=20\times 10.6 \\ I=212A \end{gathered}$$

From the problem 10.2, consider the table as,

Write the minimum fault current for the different value of input current.

I'	5	8	10	13	15
I	105	168	212	296	700

Draw the graph between the input current and primary minimum fault current as,

The relay I' current corresponding to the primary fault current I = 400 A from the above graph is 14 A.

Consider the characteristics curve of relay from the text book’s figure 10.12.

Calculate the relay input current multiple of tap setting.

$$\begin{gathered} \frac{I\text{'}}{I_p}=\frac{14}{5} \\ \frac{I\text{'}}{I_p}=2.8 \end{gathered}$$

The tap setting value is 5 A, so, the pick-up current, I_p = 5 A.

Select the curve corresponding to the TDS value and the curve comes out to be 4.

Calculate the operating time of the curve using the curve 4 and input relay multiplier 2.8. therefore, the operating time of the relay is 3.7 sec.