Insulator String Calculator: Voltage Across Each Disc and String Efficiency

See how the voltage is shared between the discs of a suspension insulator string, and how efficient the string is.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the line voltage, the number of discs and the ratio k of the capacitance to the tower to the capacitance of one disc.

The calculator takes the phase voltage, finds the voltage across every disc from the capacitance ladder, and lists them from the tower end to the line end.

It gives the string efficiency (the phase voltage over the number of discs times the voltage across the worst disc) and plots the voltage across each disc.

Formulas used

  • V_2 = V_1(1 + k)
  • V_{m+1} = V_m + k(V_1 + \dots + V_m)
  • \eta = \frac{V}{n V_n}

Worked example

With the default numbers in the calculator above:

  1. Voltage from the line to the tower: 38.11 kV
  2. Voltage across each disc as a multiple of the one nearest the tower: Factors: 1.0000, 1.1000, 1.3100, 1.6510, 2.1571
  3. Voltage across the disc nearest the tower: 5.28 kV
  4. Voltage across each disc, counted from the tower end: disc 1 5.28 kV; disc 2 5.81 kV; disc 3 6.92 kV; disc 4 8.72 kV; disc 5 11.39 kV
  5. String efficiency: 66.92 %
  6. Most stressed disc compared with an even share: 1.49 times an equal share (the disc nearest the line)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Number of discs in the string 3; Ratio of the capacitance from a disc to the tower (shunt) to the capacitance of one disc, as a fraction (often 0.1 to 0.2) 0.2.

  1. Voltage from the line to the tower: 38.11 kV
  2. Voltage across each disc as a multiple of the one nearest the tower: Factors: 1.0000, 1.2000, 1.6400
  3. Voltage across the disc nearest the tower: 9.92 kV
  4. Voltage across each disc, counted from the tower end: disc 1 9.92 kV; disc 2 11.91 kV; disc 3 16.27 kV
  5. String efficiency: 78.05 %
  6. Most stressed disc compared with an even share: 1.28 times an equal share (the disc nearest the line)

Common questions

Why is the disc nearest the line the most stressed?

Each disc has some capacitance to the tower, which takes a small charging current. These currents add up toward the line end, so the disc nearest the line carries the most.

What is a good string efficiency?

The nearer to 100 percent the better. A short string is 80 to 90 percent, and a long string drops to 60 percent or lower.

How can the efficiency be improved?

With a grading ring at the line end, by using discs of different capacitance, or by making the shunt capacitance smaller by keeping the string away from the steelwork.

What is k?

The capacitance from the metal cap of a disc to the tower, divided by the capacitance of one disc. It is usually about 0.1.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Kothari and Nagrath, Modern Power System Analysis (overhead line insulators); Wadhwa, Electrical Power Systems.

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