Improving the String Efficiency of an Insulator: 4 Methods | Electricity

The string efficiency indicates the extent of the wastage. Though string efficiency can never be made 100 per cent, an improvement in its value is necessary so as to reduce the wastage to the minimum.

Some methods used for this purpose are given below:

Method # 1. By Using Insulators with Larger Discs or by Providing Each Insulator Unit with a Metal Cap:

It is clear from the expression of string efficiency that the string efficiency increases with the decrease in value of K (i.e. the ratio of shunt capacitance to mutual capacitance). One method is to design the units such that the mutual capacitance (capacitance of each unit) is much greater than the shunt capacitance (capacitance to earth). This can be achieved by using insulators with larger discs or providing each insulator unit with a metal cap. The ratio K can be made 1/6 to 1/10 by this method.

Method # 2. By Using Longer Cross-Arms:

The ratio of shunt capacitance to mutual capacitance, K can alternatively be reduced by using longer cross-arms so that the horizontal distance from line support (pole or tower) is increased thereby decreasing the shunt capacitance. But the limitations of cost and mechanical strength of line supports do not allow the cross-arms to be too long and it has been found that in practice it is not possible to obtain the value of K less than 0.1.

Method # 3. By Capacitance Grading:

It is seen that non-uniform distribution of voltage across an insulator string is due to leakage current from the insulator pin to the supporting structure. This current cannot be eliminated. However, it is possible that discs of different capacities are used such that the product of their capacitive reactance and the current flowing through the respective unit is same.

This can be achieved by grading the mutual capacitance of the insulator units i.e., by having lower units of more capacitance—maximum at the line unit and minimum at the top unit, nearest to the cross-arm. It can be shown that by this method complete equality of voltage across the units of an insulator string can be obtained but this method needs a large number of different-sized insulator units. This involves main­taining spares of all varieties of insulator discs which is contrary to the tendency of standardization. So this method is not used in practice below 200 kV.

Consider a 4-unit string. Let C be the capacitance of the top unit and let the capacitances of others units are C₂, C₃ and C₄, as shown in Fig. 9.21.

Assume C₁ = k C

Applying Kirchhoff’s first law to node A we get,

I₂ = I₁ + i₁

or ω C₂ v = ω C v + ω C₁ v

or C₂ = C + K C = C (1 + K) … (9.11)

Applying Kirchhoff’s first law to node B we get,

I₃ = I₂ + i₂

or ω C₃ v = ω C₂ v + ω C₁ × 2 v

or C₃ = C₂ + 2 K C = C (1 + K) + 2 K C = C (1 + 3 K) … (9.12)

Applying Kirchhoff’s first law to node C we get,

I₄ = I₃ + i₃

or ω C₄ v = ω C₃ v + ω C₁ × 3 v

or C₄ = C₃ + 3 K C = C (1 + 3 K) + 3 K C = C (1 + 6 K) …(9.13)

Thus it will be possible to equalise the potential across all the units, if their capacitances are in the ratio of 1: (1 + K): (1 + 3 K): (1 + 6 K) and so on.

But in practice it is impossible to obtain such units which will have their capacitances in above ratio, although nearby results can be obtained by employing standard insulators for most of the units and employing larger units adjacent to the line.

Method # 4. By Static Shielding:

In case of capacitance grading, insulator units of different capaci­tances are used so that the flow of different currents through the respective units produce equal voltage drop. In static shielding, pin to supporting structure charging currents are exactly cancelled so that the same current flows through the identical insulator units and produce equal voltage drops across each insulator unit.

This arrangement is given is Fig. 9.22. In this method a guard or grading ring, which usually takes the form of a large metal ring surrounding the bottom unit and electrically connected to the metal work at the bottom of this unit, and therefore to the line conductor.

The guard ring screens the lower units, reduces their earth capacitance C₁ and introduces a number of capacitances between the line conduc­tor and the various insulator unit caps. These capacitances are greater for lower units and thus the voltages across them are reduced. With this method also it is impossible to obtain in practice an equal distribution of voltage but consid­erable improvements are possible.

Let the capacitances between the links and the shield be C_x, C_y and C_z respectively as shown in Fig. 9.22, and let v be the potential across each unit.

Since the capacitance of each unit is same, there­fore, their charging currents I₁, I₂, I₃, and I₄ would be same, let it be I. If C₁ = K C

Applying Kirchhoff s first law to node A we get,

I + i_x = I + i₁ or i_x = i₁ … (9.14)

Similarly, i_y = i₂ … (9.15)

and i_z = i₃ … (9.16)

Also, i₁ = ω C₁ v = ω K C v … (9.17)

i₂ = 2 ω C₁ v = 2 ω K C v … (9.18)

i₃ = 3 ω C₁v = 3 ω K C v … (9.19)

The potential causing current i_x is 3 v (voltage across three units leaving the top one).

So, i_x = ω C_x × 3 v = 3 ω C_x v … (9.20)

Comparing Eqs. (9.14), (9.17) and (9.20), we have,

3 ω C_x v = ω K C v or C_x = K C/3 … (9.21)

The potential causing current y is 2 v and therefore,

I_y =2 ω C_y v … (9.22)

Comparing Eqs. (9.15), (9.18) and (9.22) we have,

2 ω C_y v = 2 ω K C v or C_y = K C … (9.23)

The potential causing current i_z is v and therefore,

i_z = ω C_z v … (9.24)

Comparing Eqs. (9.16), (9.19) and (9.24), we have,

ω C_z v = 3 ω K C v

or C_z = 3 K C … (9.25)

In general if there are n units

i₁ = ω K C v and i_x = (n – 1) ω C_xv

or C_x = KC/ (n-1) … (2.26)

Similarly, C_y = 2KC/ (n-2) … (2.27)

and C_z = 3KC/ (n-3) … (2.28)

or The capacitance of the pth metal link to the line is given as:

C_p = pKC/ (n-p) … (2.29)