Critical Disruptive Voltage MCQ Quiz - Objective Question with Answer for Critical Disruptive Voltage - Download Free PDF

Explanation:

To find the equation for critical disruptive voltage (Vd) for local and general corona on a 3-phase overhead transmission line, we need to consider the factors affecting corona discharge. These factors include the distance between conductors (d), the radius of the conductor (r), the irregularity factor (m), and the air density correction factor (δ).

The critical disruptive voltage (Vd) is the voltage at which corona discharge starts to occur around the conductors of the transmission line. The phenomenon of corona discharge is influenced by the electric field around the conductors, which depends on the physical dimensions and environmental conditions.

For a 3-phase overhead transmission line, the expression for the critical disruptive voltage (Vd) can be derived considering the electrostatic stress around the conductors. The general formula for the disruptive voltage is given by:

\(\rm V_d = 21.1 * m * \delta * r * \ln\frac{d}{r}\)

Where:

• Vd is the critical disruptive voltage.
• m is the irregularity factor, which accounts for surface irregularities and other imperfections in the conductor.
• δ is the air density correction factor, which adjusts for variations in air density due to altitude, temperature, and humidity.
• r is the radius of the conductor.
• d is the distance between conductors.

Correct Option Analysis:

The correct option is:

Option 3: \(\rm v_d=(21.1*m*\delta*r)In\frac{d}{r}\)

This option correctly represents the equation for the critical disruptive voltage (Vd) for a 3-phase overhead transmission line. The formula takes into account the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). The natural logarithm (ln) of the ratio of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)) is used to express the electric field distribution around the conductors.

Additional Information

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

Option 1: \(\rm v_d=(21.1*m*\delta*d)In\frac{d}{r}\)

This option is incorrect because it incorrectly uses the distance between conductors (d) instead of the radius of the conductor (r) as the multiplicative factor. The correct equation should have the radius of the conductor (r) in the multiplicative term.

Option 2: \(\rm v_d=(21.1*m*\delta*r)In\frac{r}{d}\)

This option is incorrect because it reverses the ratio inside the natural logarithm. The correct ratio should be \(\frac{d}{r}\) instead of \(\frac{r}{d}\). The electric field distribution around the conductors is correctly represented by the natural logarithm of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)).

Option 4: \(\rm v_d=(21.1*m*\delta*d)In\frac{r}{d}\)

This option is incorrect for the same reasons as Option 1 and Option 2. It incorrectly uses the distance between conductors (d) as the multiplicative factor and reverses the ratio inside the natural logarithm. The correct equation should have the radius of the conductor (r) in the multiplicative term and the ratio inside the natural logarithm should be \(\frac{d}{r}\).

Conclusion:

Understanding the equation for critical disruptive voltage (Vd) for a 3-phase overhead transmission line is essential in designing transmission lines to prevent corona discharge. The correct equation, as explained, involves the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). This formula helps in predicting and mitigating the onset of corona discharge, ensuring efficient and reliable operation of the transmission line.

The correct answer is option 3.

Concept:

The critical voltage limit of a transmission line is the same as the critical disruptive voltage. 

Critical Disruptive Voltage is defined as the minimum phase to the neutral voltage required for the corona discharge(corona losses) to start.

The expression for critical disruptive voltage is given by the expression

\(V_d={mrg_0\delta ln({d\over r})}\)   .....(1)

Here, r is the radius of the conductor 

d is the interspacing between the conductors 

\(\delta\) is the air density factor

m is the irregularity factor(depends on the atmospheric conditions and decreasing in rough conditions)  

\(g_0\) is the dielectric strength of the air.

Solution:

By equation 1, we can infer that \(V_d \propto r\). So, to increase the voltage we need to increase the radius of the conductors.

Additional Information

•  There is another type of rating also for transmission lines known as critical visual voltage.
• The corona glow does not begin at the critical disruptive voltage V_c, but it begins at a higher voltage called the Visual Critical Voltage.
• It is denoted by V_v. The expression for the same is given below

\(V_v=mrg_0\delta(1+{0.3\over\sqrt {\delta r}})ln({d\over r})\)

• The power loss due to corona is given by the expression below

           \(P_c={240 \times 10^-5\over \delta}(f+25) \sqrt{r \over d}(V-V_d) kW/km/phase\)

Here, V is the phase voltage in kV and other parameters are the same as previous equations. Before calculating the power loss do check that the phase voltage is greater than the \(V_d\), if the phase voltage is less than the \(V_d\) then there is no corona loss and \(P_c =0\).

From the power loss expression, it is evident that 

\(P_c\propto (f+25)\)

The correct answer is option 3.

Concept:

The critical voltage limit of a transmission line is the same as the critical disruptive voltage. 

Critical Disruptive Voltage is defined as the minimum phase to the neutral voltage required for the corona discharge(corona losses) to start.

The expression for critical disruptive voltage is given by the expression

\(V_d={mrg_0\delta ln({d\over r})}\)   .....(1)

Here, r is the radius of the conductor 

d is the interspacing between the conductors 

\(\delta\) is the air density factor

m is the irregularity factor(depends on the atmospheric conditions and decreasing in rough conditions)  

\(g_0\) is the dielectric strength of the air.

Solution:

By equation 1, we can infer that \(V_d \propto r\). So, to increase the voltage we need to increase the radius of the conductors.

Additional Information

•  There is another type of rating also for transmission lines known as critical visual voltage.
• The corona glow does not begin at the critical disruptive voltage V_c, but it begins at a higher voltage called the Visual Critical Voltage.
• It is denoted by V_v. The expression for the same is given below

\(V_v=mrg_0\delta(1+{0.3\over\sqrt {\delta r}})ln({d\over r})\)

• The power loss due to corona is given by the expression below

           \(P_c={240 \times 10^-5\over \delta}(f+25) \sqrt{r \over d}(V-V_d) kW/km/phase\)

Here, V is the phase voltage in kV and other parameters are the same as previous equations. Before calculating the power loss do check that the phase voltage is greater than the \(V_d\), if the phase voltage is less than the \(V_d\) then there is no corona loss and \(P_c =0\).

From the power loss expression, it is evident that 

\(P_c\propto (f+25)\)

Explanation:

To find the equation for critical disruptive voltage (Vd) for local and general corona on a 3-phase overhead transmission line, we need to consider the factors affecting corona discharge. These factors include the distance between conductors (d), the radius of the conductor (r), the irregularity factor (m), and the air density correction factor (δ).

The critical disruptive voltage (Vd) is the voltage at which corona discharge starts to occur around the conductors of the transmission line. The phenomenon of corona discharge is influenced by the electric field around the conductors, which depends on the physical dimensions and environmental conditions.

For a 3-phase overhead transmission line, the expression for the critical disruptive voltage (Vd) can be derived considering the electrostatic stress around the conductors. The general formula for the disruptive voltage is given by:

\(\rm V_d = 21.1 * m * \delta * r * \ln\frac{d}{r}\)

Where:

• Vd is the critical disruptive voltage.
• m is the irregularity factor, which accounts for surface irregularities and other imperfections in the conductor.
• δ is the air density correction factor, which adjusts for variations in air density due to altitude, temperature, and humidity.
• r is the radius of the conductor.
• d is the distance between conductors.

Correct Option Analysis:

The correct option is:

Option 3: \(\rm v_d=(21.1*m*\delta*r)In\frac{d}{r}\)

This option correctly represents the equation for the critical disruptive voltage (Vd) for a 3-phase overhead transmission line. The formula takes into account the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). The natural logarithm (ln) of the ratio of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)) is used to express the electric field distribution around the conductors.

Additional Information

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

Option 1: \(\rm v_d=(21.1*m*\delta*d)In\frac{d}{r}\)

This option is incorrect because it incorrectly uses the distance between conductors (d) instead of the radius of the conductor (r) as the multiplicative factor. The correct equation should have the radius of the conductor (r) in the multiplicative term.

Option 2: \(\rm v_d=(21.1*m*\delta*r)In\frac{r}{d}\)

This option is incorrect because it reverses the ratio inside the natural logarithm. The correct ratio should be \(\frac{d}{r}\) instead of \(\frac{r}{d}\). The electric field distribution around the conductors is correctly represented by the natural logarithm of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)).

Option 4: \(\rm v_d=(21.1*m*\delta*d)In\frac{r}{d}\)

This option is incorrect for the same reasons as Option 1 and Option 2. It incorrectly uses the distance between conductors (d) as the multiplicative factor and reverses the ratio inside the natural logarithm. The correct equation should have the radius of the conductor (r) in the multiplicative term and the ratio inside the natural logarithm should be \(\frac{d}{r}\).

Conclusion:

Understanding the equation for critical disruptive voltage (Vd) for a 3-phase overhead transmission line is essential in designing transmission lines to prevent corona discharge. The correct equation, as explained, involves the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). This formula helps in predicting and mitigating the onset of corona discharge, ensuring efficient and reliable operation of the transmission line.

The correct answer is option 3.

Concept:

The critical voltage limit of a transmission line is the same as the critical disruptive voltage. 

Critical Disruptive Voltage is defined as the minimum phase to the neutral voltage required for the corona discharge(corona losses) to start.

The expression for critical disruptive voltage is given by the expression

\(V_d={mrg_0\delta ln({d\over r})}\)   .....(1)

Here, r is the radius of the conductor 

d is the interspacing between the conductors 

\(\delta\) is the air density factor

m is the irregularity factor(depends on the atmospheric conditions and decreasing in rough conditions)  

\(g_0\) is the dielectric strength of the air.

Solution:

By equation 1, we can infer that \(V_d \propto r\). So, to increase the voltage we need to increase the radius of the conductors.

Additional Information

•  There is another type of rating also for transmission lines known as critical visual voltage.
• The corona glow does not begin at the critical disruptive voltage V_c, but it begins at a higher voltage called the Visual Critical Voltage.
• It is denoted by V_v. The expression for the same is given below

\(V_v=mrg_0\delta(1+{0.3\over\sqrt {\delta r}})ln({d\over r})\)

• The power loss due to corona is given by the expression below

           \(P_c={240 \times 10^-5\over \delta}(f+25) \sqrt{r \over d}(V-V_d) kW/km/phase\)

Here, V is the phase voltage in kV and other parameters are the same as previous equations. Before calculating the power loss do check that the phase voltage is greater than the \(V_d\), if the phase voltage is less than the \(V_d\) then there is no corona loss and \(P_c =0\).

From the power loss expression, it is evident that 

\(P_c\propto (f+25)\)

Explanation:

To find the equation for critical disruptive voltage (Vd) for local and general corona on a 3-phase overhead transmission line, we need to consider the factors affecting corona discharge. These factors include the distance between conductors (d), the radius of the conductor (r), the irregularity factor (m), and the air density correction factor (δ).

The critical disruptive voltage (Vd) is the voltage at which corona discharge starts to occur around the conductors of the transmission line. The phenomenon of corona discharge is influenced by the electric field around the conductors, which depends on the physical dimensions and environmental conditions.

For a 3-phase overhead transmission line, the expression for the critical disruptive voltage (Vd) can be derived considering the electrostatic stress around the conductors. The general formula for the disruptive voltage is given by:

\(\rm V_d = 21.1 * m * \delta * r * \ln\frac{d}{r}\)

Where:

• Vd is the critical disruptive voltage.
• m is the irregularity factor, which accounts for surface irregularities and other imperfections in the conductor.
• δ is the air density correction factor, which adjusts for variations in air density due to altitude, temperature, and humidity.
• r is the radius of the conductor.
• d is the distance between conductors.

Correct Option Analysis:

The correct option is:

Option 3: \(\rm v_d=(21.1*m*\delta*r)In\frac{d}{r}\)

This option correctly represents the equation for the critical disruptive voltage (Vd) for a 3-phase overhead transmission line. The formula takes into account the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). The natural logarithm (ln) of the ratio of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)) is used to express the electric field distribution around the conductors.

Additional Information

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

Option 1: \(\rm v_d=(21.1*m*\delta*d)In\frac{d}{r}\)

This option is incorrect because it incorrectly uses the distance between conductors (d) instead of the radius of the conductor (r) as the multiplicative factor. The correct equation should have the radius of the conductor (r) in the multiplicative term.

Option 2: \(\rm v_d=(21.1*m*\delta*r)In\frac{r}{d}\)

This option is incorrect because it reverses the ratio inside the natural logarithm. The correct ratio should be \(\frac{d}{r}\) instead of \(\frac{r}{d}\). The electric field distribution around the conductors is correctly represented by the natural logarithm of the distance between conductors to the radius of the conductor (\(\frac{d}{r}\)).

Option 4: \(\rm v_d=(21.1*m*\delta*d)In\frac{r}{d}\)

This option is incorrect for the same reasons as Option 1 and Option 2. It incorrectly uses the distance between conductors (d) as the multiplicative factor and reverses the ratio inside the natural logarithm. The correct equation should have the radius of the conductor (r) in the multiplicative term and the ratio inside the natural logarithm should be \(\frac{d}{r}\).

Conclusion:

Understanding the equation for critical disruptive voltage (Vd) for a 3-phase overhead transmission line is essential in designing transmission lines to prevent corona discharge. The correct equation, as explained, involves the irregularity factor (m), the air density correction factor (δ), the radius of the conductor (r), and the distance between conductors (d). This formula helps in predicting and mitigating the onset of corona discharge, ensuring efficient and reliable operation of the transmission line.

Given that,

Diameter of conductor (D) = 1 cm

Distance between conductors (d) = 2m

Dielectric strength of air (g_max) = 30 kV/cm

\({g_{rms}} = \frac{{30}}{{\sqrt 2 }}\frac{{kV}}{{cm}} = 21.2\;kV/cm\) 

Air density factor (δ) = 0.9

Irregularity factor (m) = 0.85

The critical disruptive voltage is given by

\(= m.g\delta r\ln \left( {\frac{d}{r}} \right)\) 

\(= 0.85 \times 21.2 \times 0.9 \times 0.5 \times \ln \left( {\frac{{200}}{{0.5}}} \right)\) 

= 48.585 kV/phase.

\(\begin{array}{l} V = 21m\delta r\ln \frac{d}{r}\\ = 21 \times 1.2 \times 1 \times 0.75\ \ln \left( {\frac{{400}}{{0.75}}} \right) \end{array}\)

= 118.68 kV

Line to line voltage is = 205.55 kV

Since the operating voltage is 150 kV, the corona loss will be absent.

⇒ Corona loss = 0.