Arrester current, resistance and rating on 132 kV line

When the surge reaches the arrester, the arrester sparks over and holds the line voltage at its protective level $V_p$. It behaves as a resistance $R_a = V_p / I_a$ shunting the line, and the arrester current follows from the travelling-wave relations.

Data

• Incident surge voltage, $V_w = 3000$ kV
• Protective level of arrester, $V_p = 1700$ kV
• Line surge impedance, $Z = 300\ \Omega$
• The arrester is treated as the end (termination) of the line.

Incident current

$$I_w = \frac{V_w}{Z} = \frac{3000}{300} = 10\ \text{kA}$$

(i) Current through the arrester

The voltage at the arrester is $V_p = V_w + V_r$, so the reflected voltage is

$$V_r = V_p - V_w = 1700 - 3000 = -1300\ \text{kV}$$

The reflected current is $I_r = -V_r/Z = 1300/300 = 4.333$ kA. The arrester current is

$$\begin{aligned} I_a &= I_w + I_r = \frac{2V_w - V_p}{Z} \\ &= \frac{2 \times 3000 - 1700}{300} \\ &= 14.33\ \text{kA} \end{aligned}$$

(ii) Arrester resistance

$$R_a = \frac{V_p}{I_a} = \frac{1700}{14.333} = 118.6\ \Omega$$

(iii) Reflection and refraction coefficients

With termination $R_a = 118.6\ \Omega$ on a line of $Z = 300\ \Omega$:

$$\begin{aligned} \beta_v &= \frac{R_a - Z}{R_a + Z} = \frac{118.6 - 300}{418.6} = -0.433 \\ \alpha_v &= \frac{2R_a}{R_a + Z} = \frac{2 \times 118.6}{418.6} = 0.567 \\ \beta_i &= \frac{Z - R_a}{R_a + Z} = +0.433 \\ \alpha_i &= \frac{2Z}{R_a + Z} = \frac{600}{418.6} = 1.433 \end{aligned}$$

Check: $\alpha_v V_w = 0.567 \times 3000 = 1700$ kV $= V_p$, and $\alpha_i I_w = 1.433 \times 10 = 14.33$ kA $= I_a$.

(iv) Optimal current rating of the arrester

The arrester must discharge at least $I_a = 14.33$ kA while keeping its residual voltage at 1700 kV. The optimal (minimum) discharge current rating is therefore about 14.3 kA; in practice the next standard nominal discharge current class, 20 kA (IEC 60099-4 classes: 5, 10, 20 kA), is selected.

Answer: $I_a = 14.33$ kA, $R_a = 118.6\ \Omega$, $\beta_v = -0.433$, $\alpha_v = 0.567$, $\beta_i = 0.433$, $\alpha_i = 1.433$, rating ≈ 14.3 kA (choose the 20 kA class).