RI of 400 kV line at 0.5 MHz

RI of each phase is calculated with the CIGRE formula at 0.5 MHz, then the line RI is obtained by the CIGRE addition rule. Rainy-weather values are found by adding the CIGRE rain increment.

Data

• $H = 14$ m, $S = 11$ m, bundle $2 \times 3.18$ cm, so $d = 3.18$ cm
• $g_m$ = 17.3 kV/cm (centre) and 16.2 kV/cm (outer phases)
• Point at ground level, 30 m horizontally from one outer phase
• $RI_i = 3.5g_m + 6d - 33\log_{10}(D_i/20) - 30$ dB above 1 μV/m (average fair weather, 0.5 MHz)

  P1        P2        P3
  o--11 m---o--11 m---o           H=14 m
 ////////////////////////////////[P]
                      |<- 30 m ->|

Step 1: Distances (horizontal 30, 41, 52 m)

$$\begin{aligned} D_3 &= \sqrt{30^2 + 14^2} = 33.11\ \text{m} \\ D_2 &= \sqrt{41^2 + 14^2} = 43.32\ \text{m} \\ D_1 &= \sqrt{52^2 + 14^2} = 53.85\ \text{m} \end{aligned}$$

Step 2: Fair-weather RI of each phase

With $6d = 19.08$, $3.5 \times 16.2 = 56.70$ and $3.5 \times 17.3 = 60.55$:

$$\begin{aligned} RI_3 &= 56.70 + 19.08 - 33\log\frac{33.11}{20} - 30 = 56.70 + 19.08 - 7.22 - 30 = 38.56\ \text{dB} \\ RI_2 &= 60.55 + 19.08 - 33\log\frac{43.32}{20} - 30 = 60.55 + 19.08 - 11.08 - 30 = 38.55\ \text{dB} \\ RI_1 &= 56.70 + 19.08 - 33\log\frac{53.85}{20} - 30 = 56.70 + 19.08 - 14.20 - 30 = 31.58\ \text{dB} \end{aligned}$$

Step 3: Rainy weather

Average heavy-rain RI is about 17 dB above average fair-weather RI.

Step 4: Total RI of the line (CIGRE rule)

If one phase exceeds the others by ≥ 3 dB, the line RI is that value. Otherwise it is the mean of the two highest plus 1.5 dB. Here the two highest are almost equal:

$$\begin{aligned} RI_{fair} &= \frac{38.56 + 38.55}{2} + 1.5 = 40.05\ \text{dB} \\ RI_{rain} &= 40.05 + 17 = 57.05\ \text{dB} \end{aligned}$$

The near outer phase and the centre phase contribute almost equally: the centre phase has a higher gradient but is farther away.

Answer: phase RI (fair) = 38.56, 38.55, 31.58 dB; rain = 55.56, 55.55, 48.58 dB; line RI ≈ 40.1 dB (fair) and 57.1 dB (rain) above 1 μV/m at 0.5 MHz.