Transmission Line Parameters MCQ Quiz - Objective Question with Answer for Transmission Line Parameters - Download Free PDF

Geometry of single-phase transmission line

• A single-phase transmission line consists of two parallel conductors, one carrying the current to the load and the other returning the current. These two conductors form a loop.
• In overhead transmission lines, conductors are suspended parallel to each other from poles or towers.
• The arrangement of conductors is usually straight and spans across large distances.
• Since conductors are aligned in parallel and straight paths, they create a rectangular-shaped loop when seen in cross-section or 3D space.
• In contrast, a circular loop would mean the conductors are arranged in a curved or circular shape, which does not happen in typical power transmission.

Loop Inductance in a Two-Wire Line

The given image represents a group of two conductors. This group of conductors forms a loop inductance in a single-phase two-wire line.

When alternating current flows through the two conductors of a transmission line, each conductor generates a magnetic field, which results in self-inductance and mutual inductance effects. 

The total loop inductance (L_loop) is the inductance experienced by the complete path of current flow, which includes both conductors. It is given by: 

This means that in a single-phase two-wire system, the inductance of one conductor contributes half of the total loop inductance.

Explanation:

Line Impedance in Transmission Lines

Definition: Line impedance is a term used in electrical engineering to describe the combination of a transmission line's resistance (R), inductance (L), and capacitance (C), which collectively influence the voltage drop along the line and its ability to transfer power efficiently. This concept is crucial in the design and analysis of power transmission systems.

Components of Line Impedance:

• Resistance (R): The opposition to the flow of current in the transmission line, caused by the inherent resistive properties of the conductor material. Resistance leads to power losses in the form of heat.
• Inductance (L): The property of the transmission line that opposes changes in current flow, causing the storage of energy in a magnetic field. Inductance can cause voltage drops and phase shifts between voltage and current.
• Capacitance (C): The ability of the transmission line to store energy in an electric field, due to the potential difference between conductors. Capacitance can influence the charging current and voltage distribution along the line.

Effects of Line Impedance:

• Voltage Drop: As current flows through the transmission line, the impedance causes a voltage drop. This drop is a function of the current and the impedance, leading to a reduction in the voltage delivered at the receiving end.
• Power Losses: The resistive component of impedance results in power losses, primarily in the form of heat. These losses reduce the efficiency of power transmission.
• Power Transfer Capability: The overall impedance affects the line's ability to transfer power efficiently. Higher impedance can limit the amount of power that can be transmitted without excessive voltage drop or power loss.

Importance in Power Transmission:

The concept of line impedance is fundamental in the design and operation of power transmission systems. Understanding and managing impedance is crucial for ensuring efficient and reliable power delivery. Engineers must consider line impedance when determining the appropriate conductor size, material, and configuration to minimize losses and maintain voltage levels within acceptable limits.

Correct Option Analysis:

The correct option is:

Option 4: Line Impedance

This option accurately describes the combination of resistance, inductance, and capacitance in a transmission line, which collectively influence the voltage drop along the line and its ability to transfer power efficiently. Line impedance is a key parameter in the analysis and design of electrical power systems.

Additional Information

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

Option 1: Voltage Level

While the voltage level is an important factor in power transmission, it does not describe the combination of resistance, inductance, and capacitance. Voltage level refers to the potential difference between conductors, which is determined by the power system design and operating requirements.

Option 2: Line Configuration

Line configuration refers to the physical arrangement of conductors and their spacing in a transmission line. While configuration can influence impedance, it does not encompass the combined effects of resistance, inductance, and capacitance.

Option 3: Line Losses

Line losses refer to the power lost during transmission due to resistance and, to a lesser extent, other factors like corona discharge. Although related to impedance, line losses do not fully describe the concept of impedance, which includes inductance and capacitance.

Conclusion:

Understanding line impedance is essential for the efficient design and operation of power transmission systems. The combination of resistance, inductance, and capacitance affects voltage drop, power losses, and the overall ability to transfer power efficiently. By accurately considering these components, engineers can optimize transmission line performance and ensure reliable power delivery.

Explanation:

String Efficiency in Transmission Lines

Definition: String efficiency in transmission lines refers to the measure of the effectiveness of a string of insulators in distributing the voltage equally across each insulator. This concept is crucial in high-voltage transmission lines to ensure that no single insulator bears a disproportionate amount of the voltage, which could lead to failure or damage.

Purpose: The primary purpose of calculating string efficiency is to determine the capacitance of the string of insulators. By understanding the distribution of voltage along the string, engineers can design and optimize the insulator configuration to ensure reliability and longevity of the transmission line.

Working Principle: In a string of insulators, the voltage is not distributed equally across each insulator due to the presence of stray capacitances. The insulators closer to the energized conductor tend to bear a higher voltage compared to those further away. To ensure that the voltage distribution is as uniform as possible, the string efficiency must be calculated and optimized.

Advantages:

• Improves the reliability of the transmission line by preventing over-voltage stress on any single insulator.
• Enhances the lifespan of the insulators by ensuring an even distribution of electrical stress.
• Reduces the risk of insulator flashover and potential power outages.

Disadvantages:

• Calculation and optimization of string efficiency can be complex and may require sophisticated modeling and analysis tools.
• Increased initial cost due to the need for higher-quality insulators and optimized configurations.

Applications: String efficiency calculations are vital in the design and maintenance of high-voltage transmission lines, particularly in applications where reliability and safety are critical. They are used in power transmission systems, both for overhead lines and for substations.

Correct Option Analysis:

The correct option is:

Option 2: To determine the capacitance.

This option correctly identifies the purpose of calculating string efficiency. By determining the capacitance of the insulator string, engineers can ensure that the voltage is evenly distributed across each insulator, thereby enhancing the reliability and safety of the transmission line.

Additional Information

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

Option 1: To minimize line losses.

While minimizing line losses is a critical aspect of transmission line design, it is not the primary purpose of calculating string efficiency. String efficiency mainly focuses on the distribution of voltage across insulators rather than the reduction of line losses.

Option 3: To optimize conductor material.

Optimizing conductor material is related to the choice of materials used for the conductors to ensure they can carry the required current with minimal losses and at a reasonable cost. This is a separate consideration from string efficiency, which deals with the voltage distribution across insulators.

Option 4: To calculate inductance.

Inductance calculation is essential in understanding the behavior of transmission lines, particularly in terms of their impedance and how they respond to changes in current. However, this is not directly related to the purpose of calculating string efficiency, which is concerned with the voltage distribution across insulators.

Conclusion:

Understanding string efficiency is crucial for the design and maintenance of high-voltage transmission lines. By ensuring an even distribution of voltage across the string of insulators, engineers can enhance the reliability and safety of the transmission system. This, in turn, helps prevent insulator failure and potential power outages. While other aspects such as minimizing line losses, optimizing conductor material, and calculating inductance are important in transmission line design, they are not the primary focus of string efficiency calculations.

Explanation:

Transmission Efficiency of Short Transmission Lines

Definition: Transmission efficiency in the context of electrical power systems refers to the ratio of the power received at the receiving end of the transmission line to the power sent from the transmitting end. This efficiency indicates how effectively the transmission line conveys electrical power from the source to the load, factoring in the losses that occur during transmission.

Formula: The correct formula for calculating the transmission efficiency of short transmission lines is:

Efficiency = (Received power / Transmitted power) × 100

This formula expresses the efficiency as a percentage, which is a common practice in engineering to provide a clear and easily comparable value.

Working Principle: In an electrical transmission system, power is transmitted over lines from a generation station to various load centers. During this process, some power is inevitably lost due to the resistance of the conductors, inductive and capacitive effects, and other factors. The efficiency of the transmission line is a measure of the effectiveness with which the power is transmitted, taking into account these losses.

Detailed Explanation:

To understand why the given formula is correct, let's break down the components:

• Received Power (P_r): This is the power that reaches the load or the receiving end of the transmission line. It is the useful power that can be used by consumers or further processed.
• Transmitted Power (P_t): This is the power that is sent from the transmitting end, usually from a power plant or a substation. This is the initial power before any losses occur in the transmission process.

The formula essentially compares the power output (received power) to the power input (transmitted power). By multiplying the ratio by 100, we convert this value into a percentage, making it more intuitive and easier to understand.

For example, if a transmission line transmits 1000 MW of power and 950 MW is received at the load end, the transmission efficiency would be calculated as:

Efficiency = (950 MW / 1000 MW) × 100 = 95%

This means that 95% of the transmitted power successfully reaches the load, while 5% is lost in the transmission process.

Advantages of the Formula:

• Simplicity: The formula is straightforward and easy to apply, making it practical for engineers and technicians to quickly assess the efficiency of transmission lines.
• Clarity: Expressing efficiency as a percentage provides a clear and easily understandable measure of performance.

Correct Option Analysis:

The correct option is:

Option 4: Efficiency = (Received power / Transmitted power) × 100

This option correctly represents the formula for calculating the transmission efficiency of short transmission lines. By dividing the received power by the transmitted power and multiplying by 100, we obtain the efficiency as a percentage.

Additional Information

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

Option 1: Efficiency = 1 - (Received power / Transmitted power)

This formula is incorrect because it does not appropriately represent the concept of efficiency. Subtracting the ratio of received power to transmitted power from 1 does not yield a meaningful efficiency value and can result in a negative efficiency value, which is not logical in the context of transmission efficiency.

Option 2: Efficiency = (Transmitted power - Received power) / Transmitted power

This formula calculates the proportion of power lost during transmission but does not directly represent efficiency. Instead, it provides the loss factor, which can be useful for other analyses but is not a measure of transmission efficiency.

Option 3: Efficiency = Transmitted power / Received power

This option is incorrect because it inverts the ratio. Efficiency should be the received power divided by the transmitted power, not the other way around. Using this incorrect ratio would yield a value greater than 1 (or 100%) in most cases, which is not a feasible representation of efficiency.

Conclusion:

Understanding the correct formula for calculating the transmission efficiency of short transmission lines is crucial for accurately assessing the performance of electrical power transmission systems. The formula Efficiency = (Received power / Transmitted power) × 100 effectively captures the essence of transmission efficiency, providing a clear and practical measure of how well power is conveyed from the source to the load. By evaluating the other options, it becomes evident that they do not appropriately represent transmission efficiency, making Option 4 the correct and most logical choice.

Loop inductance of a single-phase two-wire line

Considered a single-phase line consisting of two conductors (phase and neutral) a and b of equal radius r. They are situated at a distance D meters. The cross sections of conductors are shown in the diagram below.

Let the current flow in the conductors are opposite in direction so that one becomes the return path for the other.

The flux linkages of conductor ‘a’ is given by the formula:

I_a =+I , I_b = -I, D_aa = r', D_ab = D

Inductance per conductor in a three-phase line (symmetrical)

Let the spacing between the conductors be D and the radius of each conductor, r. The flux linkages of conductor a is given by the equation:

The flux linkages of the conductor ‘a’ is given by the formula:

Where D_aa = r', 
D_ab = D_bc =  D_ac = D

Now from 3 -ϕ,3 wire system

I_a + I_b + I_c = 0
I_a = - (Ib + Ic)

,

Where L_a is the inductance per conductor in a three-phase line 

From equations (1) and (2),

Inductance per conductor in a 3-phase line = (1 / 2) times loop inductance in 1 phase.

ABCD Parameter:

We know that the ABCD parameter of the transmission line

A = D

AD – BC = 1

Conditions of reciprocity and symmetry in terms of different two-port parameters are:

Concept:

The capacitance between the conductors of a 1-ϕ, 2- long solid conductors transmission line:

D = distance of separation between two long solid conductors

r = radius of each long solid conductor 

q_A, q_B  = Charge across A and B conductors

The standard result for the capacitance between the conductors

C_AB = q_A / V_AB 

= q_B / V_BA 

= π ϵ_r ϵ_∘ / ln(D / r)       .....( i )

Calculations:

ϵ∘ = 8.85 × 10^-12 

ϵ_r  = 1 (for air)

π = 3.14

ln (D / r) = 2.303 log (D / r)

From equation ( i )

CAB = (3.14 × 8.85 × 10-12 × 1) / (2.303 log (D / r)) F/m

CAB = 

Self GMD or GMR:

• Self GMD is also called GMR. GMR stands for Geometrical Mean Radius. 
• GMR is calculated for each phase separately.
• self-GMD of a conductor depends upon the size and shape of the conductor
• GMR is independent of the spacing between the conductors.

GMD:

• GMD stands for Geometrical Mean Distance.
• It is the equivalent distance between conductors.
• GMD depends only upon the spacing 
• GMD comes into the picture when there are two or more conductors per phase.​

The inductance of the single-phase two-wire line is

  H/m

GMD = Mutual Geometric Mean Distance = D

GMR = 0.7788r

r = Radius of the conductor​

The capacitance between two conductors is

  F/m

In the calculation of the capacitance, the inner radius of the conductor not considered

Therefore, The self GMD method is used to evaluate Inductance only.

Important Points

• The inductance of the hollow conductor is less when compared to the solid conductor.
• A bundled conductor reduces the reactance of the electric transmission line.
• By making the bundle conductor, the geometric mean radius (GMR) of the conductor increased.

Concept:

The ABCD parameters are given by:

V₁ = AV₂ - BI₂

I₁ = CV₂ - DI₂

where, V₁ and I₁ are the input voltage and current

V₂ and I₂ are the output voltage and current

Case 1: When output current (I₂) = 0

 = Voltage ratio

 = Admittance

Case 2: When output voltage (V2) = 0

 = Impedance

 = Current ratio

Hence, option 2 is correct.

Concept:

For a triangle configuration of conductors , the mutual-GMD is given by:

Calculation:

Given;  D12 = 2.5 m, D23= 4.5 m, D₃₁ = 2 m

GMD = 2.82 m

Concept:

The capacitance between the conductors of a 1-ϕ, 2- long solid conductors transmission line:

D = distance of separation between two long solid conductors

r = radius of each long solid conductor 

qA, qB  = Charge across A and B conductors

The standard result for the capacitance between the conductors

CAB = qA / VAB 

= qB / VBA 

= π ϵr ϵ∘ / ln(D / r)       .....( i )

Calculations:

ϵ∘ = 8.85 × 10-12 

ϵr  = 1 (for air)

π = 3.14

ln (D / r) = 2.303 log (D / r)

From equation ( i )

CAB = (3.14 × 8.85 × 10-12 × 1) / (2.303 log (D / r)) F/m

CAB = 

The inductance of a transmission line is given by,

Where, d = distance between the conductors

r’ = 0.7788r

r = radius of conductors

Therefore, if we increase the spacing between the phase conductors, the value of line inductance will increase.

ABCD parameters:

ABCD parameters are generalized parameters of the transmission line. Given as

VS = A VR + B IR

IS = C VR + D IR

In matrix form,

VS = Sending end voltage

VR = Receiving end voltage

I_S = Sending end current

I_R = Receiving end current

A, B, C, D = T-parameter of transmission line

Calculation:

Given:

VS = 400 ∠0° kV 

A = D = 0.8 ∠1°

The system is under no-load condition

So, IR = 0, ⇒ VS = AVR

The receiving end voltage under no-load condition

VR = 500 ∠-1°  kV 

Additional Information 

Ferranti effect:

• The effect in which the voltage at the receiving end of the transmission line is more than the sending voltage (VR > V_s) is known as the ''Ferranti effect.''
• This type of effect mainly occurs because of the light load or open circuit at the receiving end.
• Ferranti effect is due to the charging current of the line.

How to reduce the Ferranti effect:

• This effect can be controlled by placing the shunt reactors at the receiving end of the lines.
• A shunt reactor is an inductive current element connected between line and neutral to compensate for the capacitive current from transmission lines.
• Synchronous phase modifier(SPM) is used as under excitation it works similarly to shunt reactor which absorbs lagging reactive power and delivers leading reactive power.

The value of the shunt reactor is given by 

Where A and B are the T-parameter of the transmission line.

Explanation:

The capacitance between line conductors:

The capacitance of the line conductors forms the shunt admittance. The conductance in the line is because of the leakage over the surface of the conductor. Considered a line consisting of two conductors a and b each of radius r. The distance between the conductors being D is shown in the diagram below:-

The potential difference between the conductors is:

Where,

qa = Charge on conductor A

qb = 0, due to neutral or earth.

V = the potential difference between the conductors

ε = absolute permittivity

D = distance between the conductors

The capacitance between the conductors is:

From the above two equations, we can say that the capacitances between line conductors and between conductors to neutral are not dependent on the magnetic flux lines and partial potential lines.

Hence option (2) is the correct answer.