Insulator discs per string, 180 MW over 200 km

The number of discs depends on the line voltage. So the voltage level and number of circuits are fixed first, and then the string is sized against the power-frequency (wet and dry), impulse and switching-surge withstand levels from Tables A-2 and A-3.

Step 1: Most economical voltage

The appendix prints Still's formula without its multiplier. That form gives about 39 kV, which is clearly not a transmission voltage. So the standard form with the factor 5.5 is used:

$$V = 5.5\sqrt{\frac{L}{1.6} + \frac{P\times 1000}{\cos\phi \times N_c \times 150}}\ \text{kV}$$

With $L = 200$ km, $P = 180$ MW and $\cos\phi = 0.85$:

Step 2: Technical check with SIL (Table A-1)

$$SIL = \frac{V^2}{Z_c} = \frac{V^2}{400}$$

For 200 km, interpolate between 160 km (2.25) and 240 km (1.75):

$$m.f. = 2.25 - \frac{200-160}{240-160}(2.25-1.75) = 2.0$$

Selected: 220 kV, single circuit. It is the economic voltage for $N_c = 1$ and it carries 180 MW with a margin.

Step 3: Withstand levels required (Table A-2)

For 220 kV nominal, the table row is the 255 kV maximum system voltage:

The string's flashover voltage must be at least the required withstand.

Step 4: Number of discs for each criterion (Table A-3, 254 × 154 mm discs)

1. Dry power frequency: 435 kV needs FOV ≥ 435 kV. 7 discs give 435 kV, so 7 discs.
2. Wet power frequency: 395 kV needs FOV ≥ 395 kV. 9 discs give only 370 kV and 10 discs give 410 kV, so 10 discs.
3. Impulse (lightning): 900 kV needs FOV ≥ 900 kV. 9 discs give 860 kV and 10 discs give 945 kV, so 10 discs.
4. Switching surge: take a switching surge ratio of 2.8 (usual for a 220 kV line without closing resistors).

$$\begin{aligned} V_{ph,peak} &= \frac{\sqrt{2}\times 245}{\sqrt{3}} = 200.0\ \text{kV} \\ V_{ss} &= 2.8\times 200.0 = 560.1\ \text{kV (peak)} \\ \text{Equivalent rms} &= \frac{560.1}{\sqrt{2}} = 396.1\ \text{kV} \end{aligned}$$

Comparing 396.1 kV with the wet FOV column gives 10 discs (410 kV).

Step 5: Final selection

• Governing requirement: 10 discs, set by the wet, impulse and switching-surge criteria.
• Add one disc to allow for a cracked or punctured disc in service, which keeps the withstand level intact.

Answer: 220 kV single-circuit line with 11 discs (254 × 154 mm) per suspension string, and 12 discs per tension string. The extra disc in the tension string covers its heavier mechanical duty and the greater exposure of dead-end and angle positions. The suspension string length is about $11 \times 0.154 = 1.69$ m plus hardware.

Assumptions: standard atmospheric conditions (no altitude correction) and light pollution. For heavy pollution or high-altitude routes in Nepal, add discs to meet creepage and air-density corrections.