String Efficiency MCQ Quiz - Objective Question with Answer for String Efficiency - Download Free PDF

Concept

String efficiency is the degree of capacity utilization of individual SCRs in a string of series/parallel connected SCRs. 

String Efficiency \(= {{V} \over V_1 \times N} \)

Where, V = Actual voltage of the whole string

V1 = Voltage rating of the insulator at the bottom

N = Total number of insulators in a string

The insulator at the bottom has the highest voltage drop

Calculation

Given, N = 3

V₁ = 10 kV

V = 6 + 8 + 10 = 24 kV

String Efficiency \(= {24 \over 3 \times 10} \)

String Efficiency = 0.8 = 80%

Explanation:

For a 132 kV transmission line using a suspension type insulator for overhead lines, the number of string insulators required is a critical factor for ensuring the reliability and safety of the electrical transmission. The correct option for the number of string insulators used in this scenario is option 1, which states that 12 insulators are required. Let’s delve into the details to understand why this is the correct option and analyze the other options as well.

Importance of Insulators in Transmission Lines:

Insulators play a vital role in overhead transmission lines. They provide the necessary insulation between the live conductors and the transmission towers or poles, preventing electrical discharges to the ground. They also support the weight of the conductors and withstand various mechanical stresses. The number of insulators in a string depends on several factors, including the transmission voltage, environmental conditions, and the type of insulators used.

Factors Determining the Number of Insulators:

• Voltage Level: Higher transmission voltages require more insulators in the string to provide adequate insulation. For a 132 kV transmission line, a specific number of insulators are needed to withstand the voltage without breaking down.
• Environmental Conditions: The number of insulators may vary based on the environmental conditions such as pollution, humidity, and altitude. In areas with heavy pollution or coastal regions, additional insulators may be required to prevent flashovers.
• Type of Insulator: Different types of insulators, such as porcelain or glass, might have different dielectric strengths and mechanical properties. The choice of insulator material can influence the number of insulators needed in a string.

Calculation for 132 kV Transmission Line:

For a 132 kV transmission line, the standard number of insulators used in a suspension string is typically 12. This is based on the following considerations:

• Dielectric Strength: Each insulator unit can withstand a specific voltage, typically around 11 kV to 15 kV. For 132 kV, dividing this voltage by the average withstand voltage per insulator unit gives us approximately 9 to 12 insulators. To ensure a margin of safety and account for any environmental factors, 12 insulators are used.
• Mechanical Strength: The insulators also need to support the mechanical load of the conductors, including wind and ice loads. A string of 12 insulators provides sufficient mechanical strength for these loads.
• Safety Margin: Electrical and mechanical safety margins are critical in transmission line design. Using 12 insulators ensures that the system can withstand higher than expected voltages and mechanical stresses.

Correct Option Analysis:

The correct option for the number of string insulators used for 132 kV transmission is:

Option 1: 12

This option is correct because it aligns with the standard design practice for 132 kV transmission lines, considering both electrical and mechanical requirements. Using 12 insulators ensures adequate insulation and mechanical support, providing a reliable and safe transmission line.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 4

This option is incorrect because using only 4 insulators for a 132 kV transmission line would not provide sufficient insulation. The dielectric strength of 4 insulators would be inadequate to withstand the 132 kV voltage, leading to a high risk of electrical breakdown and flashover.

Option 3: 2

This option is also incorrect. Using only 2 insulators for a 132 kV transmission line is far below the required number. Such a small number of insulators would not provide the necessary dielectric strength or mechanical support, making the transmission line highly unsafe and unreliable.

Option 4: 6

This option is incorrect as well. Although 6 insulators might provide some level of insulation, it would still be insufficient for a 132 kV transmission line. The safety margin would be too low, and the risk of electrical breakdown and mechanical failure would be high.

Conclusion:

Understanding the requirements for insulators in transmission lines is essential for ensuring the safety and reliability of electrical power systems. For a 132 kV transmission line using suspension type insulators, the standard number of insulators in a string is 12. This number provides the necessary dielectric strength, mechanical support, and safety margins to operate the transmission line reliably under various conditions. Analyzing the other options highlights the importance of adhering to standard practices and design considerations in transmission line construction.

Concept:

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

String efficiency = Voltage across the string / (Number of discs * Voltage across the disc nearest to the conductor)

For the adequate performance of transmission line, it is essential that the voltage distribution across the line should be uniform. This can be achieved by the following methods.

1) Use of longer cross arm

2) Capacitive grading

3) By using grading rings or static shielding

String efficiency:

• The voltage applied across the suspension insulator string is unequally distributed across the individual unit.
• The disc near the line conductor is extremely stressed and takes the maximum voltage.
• The voltage distribution on the insulator string determines the flashover voltage and the voltage at which the localized corona and radio interference is started.
• The string efficiency is defined as the ratio of conductor voltage to the voltage across the disc nearest to the conductor multiplied by the number of discs.

String efficiency = (conductor voltage) / (number of discs × voltage across the disc nearest to the conductor)

• String efficiency depends upon the value of shunt capacitance. Lesser the value of capacitance, the greater is the string efficiency.
• As the value of shunt capacitance approaches zero, the string efficiency approaches 100%.
• The greater the string efficiency, the more uniform is the voltage distribution in each disc insulator. 100% string efficiency implies that the potential across each disc is the same.
• In order to decrease the shunt capacitance, the distance between the insulator string and the tower should be increased, i.e. longer cross-arms should be used.

Additional Information

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\(String \;efficiency = \frac{{Voltage\;across\;the\;whole\;string}}{{n\; \times \;voltage\; across\; the\;unit\;adjacent\;to\;the\;conductor}}\)

For the adequate performance of the transmission line, it is essential that the voltage distribution across the line should be uniform. This can be achieved by the following methods.

1) Use of longer cross arm

2) By grading the insulator

3) By using grading rings or static shielding

Concept:

String Efficiency (η):

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\( \eta= \frac{V}{{n\; \times\; V_n}}\)

Where,

V is the voltage across the string.
Vn is the voltage across the bottom disc near to conductor
n is the number of the disc in a string

Application:

Voltage of disc nearest to conductor V₂ = V₁(1 + K)

Disc capacitance ratio K = 0.1

V₂ = V₁ (1 + 0.1) = 1.1 V₁

V₃ = V₂ + (V₁ + V₂) K = 1.1V₁ + 2.1V₁(0.1) = 1.31 V₁

String Efficiency = \(\frac{{{V_1} + {V_2} + {V_3}}}{{n{V_3}}} \times 100 = \frac{{{V_1} + 1.1{V_1} + 1.31{V_1}}}{{3 \times 1.31{V_1}}} = \frac{{3.41}}{{3.9}} = 89\;\% \)

Concept:

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

String efficiency = (conductor voltage)/(number of discs × voltage across the disc nearest to the conductor)

For the adequate performance of transmission line, it is essential that the voltage distribution across the line should be uniform. This can be achieved by the following methods.

1) Use of longer cross arm

2) Capacitive grading

3) By using grading rings or static shielding

Calculation:

Given that,

Let the total voltage = V

Voltage across the bottom most unit = 0.33V

Number of insulators (n) = 4

String efficiency \( = \frac{V}{{4\; \times\; 0.33V}} \times 100 = 75\% \)

Concept:

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

String efficiency = (conductor voltage)/(number of discs × voltage across the disc nearest to the conductor)

For the adequate performance of transmission line, it is essential that the voltage distribution across the line should be uniform. This can be achieved by the following methods.

1) Use of longer cross arm

2) Capacitive grading

3) By using grading rings or static shielding

Calculation:

Given that,

Let the total voltage = V

Voltage across the bottom most unit = 0.33V

Number of insulators (n) = 4

String efficiency \( = \frac{V}{{4\; \times\; 0.33V}} \times 100 = 75\% \)

Important points of the voltage distribution across string of suspension insulators:

• Due to the presence of a shunt capacitor, the voltage across the suspension insulators does not distribute itself uniformly across each disc. 
• The voltage across the nearest disc to the conductor is maximum than the other discs.
•  The unit nearest to the conductor is under maximum electrical stress and is likely to be punctured.
• In the case of D.C voltage, the voltage across each unit would be the same. It is because insulator capacitance is ineffective for D.C.

Additional Information

String efficiency of Suspension:

It is define as the ratio of voltage across the whole string to the product of the number of insulator discs and the voltage across the insulator disc nearest to the line conductor.

\(\% String\;efficieny = \;\frac{{V_A}}{{n × V_B}} × 100\)

VA = voltage across the string

VB = voltage across disc nearest to the conductor

n = number of insulator disc

Method of improving string efficiency: 

1) Capacitance grading or grading of the unit

2) Using Gaurd ring

Concept:

String Efficiency (η):

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\( \eta= \frac{V}{{n\; \times\; V_n}}\)

Where,

V is the voltage across the string.
Vn is the voltage across the bottom disc near to conductor
n is the number of the disc in a string

Calculation:

Given that,

Let the total voltage = V 

Voltage across the bottom most unit = 20 kV

Number of insulators (n) = 3

String efficiency = (conductor voltage)/(number of discs × voltage across the disc nearest to the conductor)

String efficiency \( = \frac{V}{{3\; \times\; 20\times 10^3}} \times 100 = 75\% \)

V = 45 kV

String efficiency is independent of frequency. Hence when we change the frequency from 50 Hz to 60 Hz it doesn't change.

Explanation:

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\(String \;efficiency = \frac{{Voltage\;across\;the\;whole\;string}}{{n\; \times \;voltage\; across\; the\;unit\;adjacent\;to\;the\;conductor}}\)

For the adequate performance of the transmission line, it is essential that the voltage distribution across the line should be uniform. This can be achieved by the following methods.

1) Use of longer cross arm

2) By grading the insulator

3) By using grading rings or static shielding

Concept:

String Efficiency (η):

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\( η= \frac{V}{{n\; \times\; V_n}}\)

Where,

V (= V1 + V2 + .... Vn) is the voltage across the string.
Vn is the voltage across the bottom disc near to conductor
n is the number of the disc in a string

Calculation:

Given

n = 2

 \({V_2} = 2{V_1}\)

\(\Rightarrow \% η_{st} = \frac{{{V_1} + {V_2}}}{{2 \times {V_2}}} \times 100\)

\(\Rightarrow \% η_{st} = \frac{{{V_1} + 2{V_1}}}{{2 \times 2{V_1}}} \times 100\)

= 75%

Concept:

String Efficiency (η):

The string efficiency is defined as the ratio of voltage across the string to the product of the number of strings and the voltage across the unit adjacent string.

\( \eta= \frac{V}{{n\; \times\; V_n}}\)

Where,

V is the voltage across the string.
V_n is the voltage across the bottom disc near to conductor
n is the number of the disc in a string

Calculation:

Given that,

V = a

n = b

V_n = c

From the above concept,

\( \eta= \frac{V}{{n\; \times\; V_n}}= \frac{a}{{b\; \times\; c}}\)

Hence, String efficiency is a / (bc)

Concept:

The string efficiency of the overhead transmission line is given by:

\(η = {V_1+V_2+.......V_n\over n\times V_n}\)

where, n = No. of insulator disc in the string

V_n = Voltage across the n^th disc

Explanation:

If the voltage across each disc insulator in a string is equal, then:

\(V_1+V_2+.......V_n = nV_n\)

\(η = {n\times V_n\over n\times V_n}\)

η = 1

Method to increase string efficiency:

1.) By using longer cross-arms: 

• The value of string efficiency depends upon the value of K i.e., the ratio of shunt capacitance to mutual capacitance.
• The lesser the value of K, the greater the string efficiency, and the more uniform the voltage distribution.
• The value of K can be decreased by reducing the shunt capacitance.
• In order to reduce shunt capacitance, the distance of the conductor from the tower must be increased i.e., longer cross-arms should be used.
• However, the limitations of cost and strength of the tower do not allow the use of very long cross-arms.

2.) By grading the insulators:

• In this method, insulators of different dimensions are so chosen that each has a different capacitance.
• The insulators are capacitance graded i.e. they are assembled in the string in such a way that the top unit has the minimum capacitance, increasing progressively as the bottom unit (i.e., nearest to the conductor) is reached.
• Since voltage is inversely proportional to capacitance, this method tends to equalize the potential distribution across the units in the string.

3.) By using a guard ring:

• The potential across each unit in a string can be equalized by using a guard ring which is a metal ring electrically connected to the conductor and surrounding the bottom insulator.
• The guard ring introduces capacitance between metal fittings and the line conductor.
• The guard ring is contoured in such a way that shunt capacitance currents are equal to metal fitting line capacitance currents. 
• The result is that the same charging current flows through each unit of string.
• Consequently, there will be uniform potential distribution across the units.

Concept:

Potential Distribution over Suspension Insulator String:

• A string of suspension insulators consisting of a number of porcelain discs connected in series with each other by means of metallic links.
• Each disc form a capacitor C known as mutual capacitance.
• The capacitance also exists between metal fitting of all disc to the tower which is known as shunt capacitance C₁.
• The shunt capacitance cause, the voltage across each of the discs will be different.
• The lower disc will have maximum voltage stress.
   

Consider a two-string suspension insulator

The voltage across each insulator is shown in such a way that,

V₂ > V₁

And, V = V₁ + V₂ …. (1)

Let us assume that, C₁ = KC

Apply KCL at node A,

I₂ = I₁ + i₁

V₂ωC = V₁ωC + V₁ωC₁

V₂ωC = V₁ωC + V₁ωKC

∴ V₂ = V₁ (1+K)

And, \({V_1} = \frac{{{V_2}}}{{\left( {1 + K} \right)}}\)

From equation (1)

V = V₁ + V₂

\(V = \frac{{{V_2}}}{{\left( {1 + K} \right)}} + {V_2}\)

Calculation:

Given,

C = X

C₁ = 0.1 X

K = C₁ / C

⇒ K = 0.1

There is 2 suspension insulator, therefore maximum voltage will be across the lower unit.

V₂ = 12.1 kV

From the above concept,

\(V = \frac{{{V_2}}}{{\left( {1 + K} \right)}} + {V_2} = \frac{{12.1}}{{\left( {1 + 0.1} \right)}} + 12.1 = 23.1\;kV\)

The insulator string can withstand 23.1 kV maximum voltage.