String Efficiency MCQ Quiz in मल्याळम - Objective Question with Answer for String Efficiency - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

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 + .... V_n) 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,

V₁ = V₂ = ... = V_n = x

Hence, V = x + x + x .... x = nx

nV_n = nx

Hence, η = nx/nx = 1

Hence, string efficiency will be 100%.

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,

n = 6

Vn = V₆ = 0.2 V

\(\% {\eta _{string}} = \frac{V}{{6 \times {V_6}}} \times = \frac{V}{{6 \times 0.2V}} \times 100\)

= 83.33%

→ Now if we apply DC voltage, Since there are no currents flowing in any part of the insulator circuit (assuming infinite leakage resistance) Capacitor blocks DC and allows only AC. So capacitors do not play a role in Dc supply,

→ The voltage across each of the equal capacitance units is equal, i.e. uniform voltage distribution exists, the string efficiency becomes 100%.

Additional Information

String efficiency(η) 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.

\(\% η = \frac{{V_s}}{{n\; × \;V_n}} × 100\)

Vs = voltage across the string

Vn = 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

V₁ = 8 kV, V₂ = 11 kV

V₃ = V₁ (K² + 3k + 1)

\(K = \frac{{{V_2} - {V_1}}}{{{V_1}}} = \frac{{11 - 8}}{8} = 0.375\)

V₃ = 8 (0.375² + 3(0.375) + 1)

= 18.125 kV

V_ph = V₁ + V₂ + V₃

= 8 + 11 + 18.125 = 37.125 kV

\({V_L} = \sqrt 3 \times 37.125 = 64.3\;kV\)

String efficiency, \(\eta = \frac{{{V_{ph}}}}{{3{V_3}}} = \frac{{37.125}}{{3 \times 18.125}} \times 100\)

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) 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.

\(\% η = \frac{{V_s}}{{n\; × \;V_n}} × 100\)

V_s = voltage across the string

V_n = voltage across disc nearest to the conductor

n = number of insulator disc

Calculation:

Given that 

Voltage across string V_s = 38 kV

Number of disc n = 4

voltage across disc nearest to conductor V_n = 12 kV

\(\% η = \frac{{38}}{{4 \;\times \;12}} \times 100 = 79.16\% \)

Key Points

Method of improving string efficiency: 

1) Capacitance grading or grading of the unit

2) Using Gaurd ring

Concept:

String Efficiency of SCR: String Efficiency of SCR is the degree of capacity utilization of individual SCRs in a string of series/parallel connected SCRs. String efficiency is always less than 1.

String Efficiency \(= {{V} \over V_1 \times N} = {{I} \over I_1 \times N}\)

Where,

• V = Actual voltage of the whole string
• I = Actual current of the whole string
• V1 = Voltage rating of one SCR
• I1 = Current rating of one SCR
• N = Total number of SCRs in a string
   

Derating Factor (DFR) of SCR: Derating Factor is the amount by which the string efficiency deviates from unity or 100%.

DFR = [1 – String Efficiency]

DFR = [100 – % String Efficiency]

• Derating Factor gives an idea of unused capacity available in a sting of SCRs.
• That's why it is a measure of the reliability of string.
• The lesser the value of sting efficiency, the lesser will be voltage / current sharing by the individual SCRs.
• It means, more unused capacity will be available with the string and hence more DFR.
• But lesser string efficiency increases the cost of string.
• So that a compromise is made in between economy and reliability by properly designing a value of string efficiency.

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 forms 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, V1=V2(1+K)" tabindex="0">V₁=V₂(1+K)V₁=V₂(1+K)

From equation (1)

V = V1 + V2

If we consider three disc system then

V2 = V1 (1+K)

V₃ = V₂ + (V₁ + V₂) K

String Efficiency  \(\eta_{st}=\frac{{{V_1} + {V_2} + {V_3}}}{{n{V_3}}} \times 100\)

n = number of discs = 3 

V=V2(1+K)+V2" tabindex="0">V=V2(1+K)+V2Calculation:

Given,

K = C1 / C

⇒ K = 0.11

from concept

V₂ = V₁ (1 + 0.11) = 1.11 V₁

V₃ = V₂ + (V₁ + V₂) K = 1.11V₁ + 2.11V₁(0.11) = 1.342 V₁

\( \eta_{st}=\frac{{{V_1} + {V_2} + {V_3}}}{{n{V_3}}} \times 100 = \frac{{{V_1} + 1.11{V_1} + 1.342{V_1}}}{{3 \times 1.342{V_1}}} = \frac{{3.452}}{{4.026}} = 85.74\;\% \)

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 number of discs.

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

Analysis:

• It depends on the number of discs in the string
• It 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 to zero, the string efficiency approaches to 100%.
• 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.

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 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