Question

Three-zone mho relays are used for transmission line protection of the power system shown in Figure 10.25. Positive-sequence line impedances are given as follows.

Line Positive-Sequence Impedance,$\mathit{\Omega }$

1-2 6+j60 2-3 4+j40 2-4 5+j50

Rated voltage for the high-voltage buses is$\mathbf{500}\mathbf{}\mathit{k}\mathit{V}$. Assume a 2500 : 5 CT ratio and a 4500 : 1 VT ratio at B12. (a) Determine the settings ${\mathit{Z}}_{\mathbf{t}\mathbf{1}}\mathbf{}\mathbf{}\mathbf{,}\mathbf{}\mathbf{}{\mathit{Z}}_{\mathbf{t}\mathbf{2}}$and ${\mathit{Z}}_{\mathbf{t}\mathbf{3}}$ for the mho relay at B12. (b) Maximum current for line 1–2 under emergency loading conditions is 1400 A at 0.90 power factor lagging. Verify that B12 does not trip during emergency loading conditions.

Short answer

Answer

(a)

The value of impedance setting $Z_{t1}$for the mho relay at B12 is $0.533+j5.33\Omega$.

The value of impedance setting $Z_{t2}$for the mho relay at B12 is.

The value of impedance setting $Z_{t3}$for the mho relay at B12 is$1.33+j13.33\Omega$.

(b)

The value of secondary impedance viewed by B12 during the emergency condition is $Z\text{'}=22.91\angle 25.8^{°}$.

Step-by-step solution

Write the given data from the question.

The given value of Positive-Sequence Impedance of line 1 - 2 is 6 + j60.

The given value of Positive-Sequence Impedance of line 2 - 2 is 4 + j40.

The given value of Positive-Sequence Impedance of line 2 - 4 is 4 + j50.

The rated value of high-voltage buses is 500 kV.

Assume a 2500 : 5 CT ratio and a 4500:1VT ratio at B12.

The maximum line current 1-2 under emergency loading conditions is 1400 A at 0.90lagging power factor.

Determine the formula of impedance setting and secondary impedance for the relay at B12 during the emergency condition.

Write the formula of impedance setting for the mho relay at B12.

$\mathit{Z}\mathbf{\text{'}}\mathbf{=}\frac{\mathbf{Z}}{\mathbf{9}}$ …… (1)

Here, Z is secondary impedance relay.

Write the formula of secondary impedance viewed by B12 during the emergency condition.

$\mathit{Z}\mathbf{\text{'}}\mathbf{=}\left(\frac{\overline{V_{LN}}}{I_L}\right)\left(\frac{}{15}\right)$ …… (2)

Here, $\overline{{\mathbf{V}}_{\mathbf{LN}}}$is rated voltage and $\overline{I_{\mathbf{L}}}$is maximum line current.

(a) Determine the value of impedance setting for the mho relay at B12.

Refer to Figure 10.25 in the textbook.

Determine the secondary impedance as seen by the impedance relay at B12.

$Z\text{'}=\frac{{\mathrm{V}}_{{}_{\mathrm{LN}}}^{\text{'}}}{I_{{}_L}^{\text{'}}}$

Here, ${\mathbf{V}}_{{}_{\mathbf{LN}}}^{\mathbf{\text{'}}}$is rated voltage and $I_{{}_{\mathbf{L}}}^{\mathbf{\text{'}}}$is maximum line current.

Substitute $\frac{V_{LN}}{\left({\displaystyle \frac{4500}{1}}\right)}$for $V_{LN}^{\text{'}}$into above equation.

$$\begin{gathered} Z\text{'}=\frac{\left({\displaystyle \stackrel{V_{LN}}{\left(\frac{4500}{1}\right)}}\right)}{\left({\displaystyle \frac{I_L}{\left({\displaystyle \frac{2500}{5}}\right)}}\right)} \\ =\left(\frac{V_{LN}}{I_L}\right)\left(\frac{1}{9}\right) \\ =\frac{Z}{9} \end{gathered}$$

Set the B12 zone 1 relay for a line 1 - 2 to reach 80%. As a result, the line's effective impedance for the relay is 80%of its overall impedance.

Determine the impedance setting $Z_{t2}$ for the mho relay at B12.

Substitute 0.8(6 + j60) for Z into equation (1).

$$\begin{gathered} Z_{t2}=\frac{1.2\left(6+j60\right)}{9}\Omega \\ =\frac{7.2+j72}{9}\Omega \\ =0.8+j8\Omega \end{gathered}$$

Set the B12 zone 2 relay for a line 1 - 2 to reach 120%. As a result, the line's effective impedance for the relay is 120%of its overall impedance.

Determine the impedance setting $Z_{t3}$ for the mho relay at B12.

Substitute 1.2(6 + j60) for Z into equation (1).

$$\begin{gathered} Z_{t2}=\frac{1.2\left(6+j60\right)}{9}\Omega \\ =\frac{7.2+j72}{9}\Omega \\ =0.8+j8\Omega \end{gathered}$$

Set the B12 zone 3 relay for a line 1 - 2 to reach 100% and a line 2 - 4 to reach 120%. As a result, the line's effective impedance for the relay is 120%of its overall impedance.

Determine the impedance setting $Z_{t3}$ for the mho relay at B12.

Substitute 1.0(6 + j60) + 1.2 (5 + j50) for Z into equation (1).

$$\begin{gathered} Z_{t3}=\frac{1.0\left(6+j60\right)}{9}+\frac{1.2\left(5+j50\right)}{9}\Omega \\ =\frac{6+j60+6+j60}{9}\Omega \\ =\frac{12+j120}{9}\Omega \\ =1.33+j13.33\Omega \end{gathered}$$

Therefore, the impedance setting for the mho relay at B 12 are:”

$$\begin{gathered} Z_{t1}=0.533+j5.33\Omega \\ {Z}_{t2}=0.8+j8\Omega \\ {Z}_{t1}=1.33+j13.33\Omega \end{gathered}$$

(b) Determine the value of secondary impedance viewed by B12 during the emergency condition 1.

Draw a circuit diagram of showing characteristics of the impedance relay as shown in below.

Figure 1

Determine the value of secondary impedance viewed by B12 during the emergency condition.

Substitute $\frac{500\times {10}^3}{\sqrt{3}}\angle 0^{°}$for $\overline{V_{LN}}$and $1400\angle -{\cos }^{-1}0.9$for $I_L$into above equation (2).

$$\begin{gathered} Z\text{'}=\left(\frac{{\displaystyle \frac{500\times {10}^3}{\sqrt{3}}}\angle 0^{°}}{1400\angle -{\cos }^{-1}0.9}\right)\left(\frac{1}{9}\right) \\ =22.91\angle 25.8^{°} \end{gathered}$$

The impedance exceeds the zone 3 settings of $1.33+j13.3=13.39\angle 84.3^{°}\Omega$for B12.

The impedance during an emergency, as shown in Figure 1, is outside the trip region of this three-zone mho relay. As a result, the relay does not trip.