All questions of Characteristics & Performance of Transmission Lines for Electrical Engineering (EE) Exam

Transmission Line Classification
Transmission lines are categorized based on their length and the electrical characteristics they exhibit. The classifications include short, medium, and long transmission lines.
Short Transmission Lines
- Length: Typically up to 50 km.
- Characteristics: In this range, the line behaves like a pure resistance and reactance.
- Analysis: The voltage drop and power losses can be calculated using simple series impedance models.
Medium Transmission Lines
- Length: Ranges from 50 km to 150 km.
- Characteristics: These lines exhibit significant capacitive effects, requiring more complex calculations.
- Analysis: The performance can be determined using the nominal π or T model, accounting for both resistance and reactance.
Long Transmission Lines
- Length: Greater than 150 km.
- Characteristics: These lines require full transmission line theory to analyze due to the influence of distributed capacitance and inductance.
- Analysis: The equations become more complex, involving hyperbolic functions to calculate voltages and currents at different points along the line.
Correct Answer: Short Transmission Line
In the context of the question, a transmission line length of up to 80 km is categorized as a short transmission line. The reasoning is based on the defined length ranges for transmission lines:
- Up to 50 km: Clearly classified as short.
- 50 km to 150 km: Classified as medium.
Since 80 km falls into the range that is predominantly considered medium but is closer to the short category, the correct classification aligns with the principles of short transmission lines, which dominate in performance characteristics up to 80 km. Thus, the answer is option 'A'.

The surge impedance of a transmission line is a measure of its ability to transmit electrical energy without reflecting any energy back to the source. It is represented by the symbol Z0 and is typically given in ohms. The surge impedance is determined by the physical characteristics of the transmission line, such as its length, capacitance, and inductance.

Given that the surge impedance of a 400 km long overhead transmission line is 400 ohms, we can calculate the surge impedance for a 200 km length of the same line.

To calculate the surge impedance for a 200 km length, we can use the formula:

Z0 = sqrt(L/C)

where L is the inductance per unit length and C is the capacitance per unit length.

Since the length of the line is halved, the inductance and capacitance per unit length will also be halved.

Let's assume that the inductance and capacitance per unit length for the 400 km line are L1 and C1, respectively. Therefore, for the 200 km line, the inductance and capacitance per unit length would be L2 = L1/2 and C2 = C1/2.

Substituting these values into the formula, we get:

Z0 = sqrt(L2/C2)
= sqrt((L1/2)/(C1/2))
= sqrt(L1/C1)
= 400 ohms (given)

Therefore, the surge impedance for the 200 km length of the transmission line is also 400 ohms, which corresponds to option C.

Surge Impedance Loading (SIL)

SIL refers to the maximum power that can be transmitted through a transmission line without causing excessive voltage fluctuations or damage to the line. It is typically expressed in megawatts (MW) and is influenced by factors such as line length, voltage level, and line parameters.

Given Information
- Voltage level: 400 kV
- Frequency: 50 Hz
- Line type: Overhead single circuit transmission line

Calculating Surge Impedance

The surge impedance of a transmission line can be calculated using the formula:

SIL = (V^2) / Zs

Where:
- SIL is the surge impedance loading
- V is the line voltage
- Zs is the surge impedance of the line

The surge impedance of a transmission line can be calculated using the formula:

Zs = (V^2) / S

Where:
- Zs is the surge impedance
- V is the line voltage
- S is the line charging capacity

Calculating Surge Impedance Loading

To calculate the surge impedance loading, we need to determine the surge impedance first. The line charging capacity, S, is typically given in pico-farads per kilometer (pF/km) and can be approximated using empirical formulas.

Since the line is a 400 kV, 3-phase transmission line, we can assume an approximate value for S. For a 400 kV line, the typical value of S is around 0.1 pF/km.

Considering the line length can be assumed to be 100 km (for simplicity), we can calculate the surge impedance using the formula:

Zs = (V^2) / S
= (400,000^2) / (0.1 x 100)
= 160,000,000 / 10
= 16,000,000 ohms

Now that we have the surge impedance, we can calculate the surge impedance loading using the formula:

SIL = (V^2) / Zs
= (400,000^2) / 16,000,000
= 160,000,000,000 / 16,000,000
= 10,000 MW

Therefore, the approximate value of the surge impedance loading for a 400 kV, 3-phase 50 Hz overhead single circuit transmission line is 10,000 MW.

Conclusion

The correct answer is option B, 400 MW, which is incorrect. The correct answer is 10,000 MW.

Ferranti Effect:
The Ferranti effect is a phenomenon that occurs in long transmission lines when the receiving end voltage is higher than the sending end voltage. It is caused by the distributed capacitance of the transmission line.

Explanation:
When power is transmitted over a long transmission line, the line itself has capacitance due to the isolation between the conductors and the ground. This distributed capacitance allows the line to store energy in the form of electric charge.

Effect of Distributed Capacitance:
When the transmission line is lightly loaded or unloaded, the receiving end voltage is higher than the sending end voltage due to the effect of distributed capacitance. This is because the capacitance causes a leading current to flow, which leads to a voltage drop across the line impedance. This voltage drop adds to the sending end voltage and increases the receiving end voltage.

Voltage Drop Across Line Resistance:
The voltage drop across the line resistance is determined by the current flowing through the transmission line. In the case of the Ferranti effect, the receiving end voltage is higher than the sending end voltage, which means that the current flowing through the line is leading the voltage.

In-phase vs. Lagging vs. Leading:
In an AC circuit, the voltage and current can be in phase, lagging, or leading each other. In the case of the Ferranti effect, the voltage drop across the line resistance leads the receiving end voltage. This means that the current flowing through the line is leading the voltage, causing the voltage drop to also lead the receiving end voltage.

Conclusion:
During the Ferranti effect, the voltage drop across the line resistance leads the receiving end voltage. This is due to the leading current flowing through the transmission line caused by the distributed capacitance. It is important to consider the Ferranti effect in long transmission lines to ensure proper voltage regulation and stability.

Explanation:

Ferranti effect is a phenomenon of voltage rise at the receiving end of a long transmission line due to the capacitance of the line. This effect is not a problem for short transmission lines as the capacitance of the line is low.

Short Transmission Lines:

A short transmission line is a line whose length is less than 80 km (50 miles) and has a voltage level less than 69 kV. The capacitance of a short transmission line is low, so the voltage rise due to the capacitance is negligible. Therefore, Ferranti effect is not a problem for short transmission lines.

Long Transmission Lines:

A long transmission line is a line whose length is greater than 250 km (150 miles) and has a voltage level above 200 kV. The capacitance of a long transmission line is high, so the voltage rise due to the capacitance is significant. Therefore, Ferranti effect is a problem for long transmission lines.

Medium Transmission Lines:

A medium transmission line is a line whose length is between 80 km (50 miles) and 250 km (150 miles) and has a voltage level between 69 kV and 200 kV. The capacitance of a medium transmission line is moderate, so the voltage rise due to the capacitance is significant, but not as much as in the case of long transmission lines. Therefore, Ferranti effect may be a problem for medium transmission lines.

Transmission Line Having High Capacitance:

Transmission lines having high capacitance, such as underground cables, may also experience Ferranti effect. The capacitance of underground cables is much higher than overhead lines, and the voltage rise due to capacitance can be significant. Therefore, Ferranti effect is a problem for transmission lines having high capacitance.

Conclusion:

Ferranti effect is not a problem for short transmission lines as the capacitance of the line is low. It is a problem for long transmission lines and transmission lines having high capacitance. Ferranti effect may be a problem for medium transmission lines as well, but not as much as in the case of long transmission lines.

The correct answer is option D) 200 Km.

Transmission lines are used to transmit electrical power over long distances. They are an essential component of the power system infrastructure, connecting power generation sources to load centers. The length of a transmission line plays a crucial role in determining its performance and characteristics.

Transmission lines can vary in length depending on the specific requirements of the power system. Short transmission lines are typically used for local distribution, while long transmission lines are used for interconnecting different regions or countries.

In the context of this question, we are considering a long transmission line. The length of this transmission line is stated to be more than 80 Km, 50 Km, 120 Km, and 200 Km. Among these options, option D) 200 Km is the correct answer.

Explanation:
1. Transmission Line Length:
- Transmission lines can span hundreds or even thousands of kilometers.
- The length of a transmission line is determined by factors such as geographical distance, load requirements, and system planning considerations.

2. Importance of Long Transmission Lines:
- Long transmission lines are essential for transmitting power over vast distances.
- They enable the efficient transfer of electricity from power generation sources to distant load centers.
- Long transmission lines are used for interconnecting different regions or countries, facilitating the exchange of surplus power.

3. Considerations for Long Transmission Lines:
- Longer transmission lines pose certain challenges compared to shorter ones.
- The line impedance and losses increase with the length of the transmission line.
- Voltage drop and reactive power compensation become more critical for longer transmission lines.
- The choice of conductor material, tower design, and insulation also need to be carefully considered for long transmission lines.

4. Optimal Transmission Line Length:
- The optimal length of a transmission line depends on various factors, including the power system's geographic layout and load demand patterns.
- System planners and engineers analyze and optimize the transmission line length to ensure reliable and efficient power transmission.

In conclusion, the correct answer to the question is option D) 200 Km. This option represents a transmission line length that is more than the other given options, indicating a long transmission line suitable for interconnecting different regions or countries.

Characteristic Impedance Loading

The surge impedance loading of a transmission line is also known as characteristic impedance loading. It refers to the loading condition where the load impedance matches the characteristic impedance of the transmission line. The characteristic impedance is a fundamental property of the transmission line, which is determined by its physical parameters such as the resistance, inductance, and capacitance per unit length.

Understanding Surge Impedance Loading

When a transmission line is operating at its surge impedance loading, it results in maximum power transfer along the line. This is because when the load impedance matches the characteristic impedance, there is no reflection of the transmitted wave and the line is fully utilized.

Characteristics of Surge Impedance Loading

When a transmission line is operating at its surge impedance loading, the following characteristics can be observed:

1. Maximum Power Transfer: Surge impedance loading allows for maximum power transfer along the transmission line. This is achieved when the load impedance matches the characteristic impedance.

2. No Reflection: At surge impedance loading, there is no reflection of the transmitted wave. This means that the entire power is delivered to the load without any loss due to reflections.

3. Minimum Voltage Drop: Surge impedance loading minimizes the voltage drop along the transmission line. This allows for efficient power transmission over long distances.

4. No Distortion: Surge impedance loading ensures that the transmitted wave is not distorted. This is because there are no reflections to cause interference or signal distortion.

5. Efficient Energy Transfer: Surge impedance loading maximizes the efficiency of energy transfer along the transmission line. This is particularly important for long-distance power transmission systems.

Importance of Characteristic Impedance Loading

Operating a transmission line at its surge impedance loading is important for efficient and reliable power transmission. It ensures maximum power transfer, minimizes losses, and reduces the chances of signal distortion. Surge impedance loading is a key consideration in the design and operation of transmission lines to optimize their performance and efficiency.

In Conclusion

Surge impedance loading, also known as characteristic impedance loading, is the loading condition where the load impedance matches the characteristic impedance of the transmission line. This results in maximum power transfer, minimal voltage drop, and efficient energy transfer along the line. Surge impedance loading is an important concept in the design and operation of transmission lines to ensure reliable and efficient power transmission.

Introduction:
In electrical power systems, transformers are used to step up or step down voltage levels for efficient transmission and distribution of electrical energy. Transformer tap changers are essential devices that enable the adjustment of the transformer's voltage ratio to compensate for voltage variations in the power system. They are typically provided on the high voltage side of the transformer.

Explanation:
The tap changer is a device used to change the number of turns in the transformer winding connected to the primary winding or high voltage side of the transformer. It provides a means to vary the turns ratio of the transformer, allowing adjustment of the output voltage to match the desired level. This adjustment is necessary to compensate for fluctuations in the input voltage, load conditions, or to maintain voltage regulation.

Advantages of Tap Changers:
1. Voltage Regulation: Tap changers help maintain a constant output voltage by adjusting the turns ratio. This ensures that the voltage delivered to the load remains within acceptable limits.
2. Load Compensation: Tap changers allow for adjustments to compensate for variations in the load, ensuring the required voltage is supplied even under changing load conditions.
3. Voltage Control: Tap changers enable control over the output voltage, allowing for voltage changes as per system requirements.

Placement of Tap Changer:
Tap changers are typically provided on the high voltage side of the transformer. This is because the high voltage winding is usually the primary winding, and any changes made to the turns ratio on this side will directly impact the output voltage. Placing the tap changer on the high voltage side provides a more efficient and effective means of achieving the desired voltage adjustment.

Conclusion:
Transformer tap changers are important devices used to adjust the voltage ratio of a transformer. They are primarily placed on the high voltage side of the transformer to ensure accurate and efficient voltage regulation. This placement allows for easy adjustment of the turns ratio to compensate for voltage fluctuations and maintain the desired output voltage.

Surge Impedance of Cable
The surge impedance of a cable is a characteristic impedance that represents the resistance to the propagation of transient voltage signals along the length of the cable. It is an important parameter in power systems and transmission lines as it determines how effectively a cable can transmit surge currents without experiencing excessive voltage drops.

Calculation of Surge Impedance
The surge impedance of a cable is typically calculated using the formula:
Zs = √(L/C)
where:
Zs = Surge Impedance
L = Inductance per unit length of the cable
C = Capacitance per unit length of the cable

Importance of Surge Impedance
- Surge impedance is crucial in determining the ability of a cable to handle transient overvoltages and surges without damage.
- It helps in designing protection systems for the cable to prevent damage due to lightning strikes, switching surges, or other transient events.
- Surge impedance also affects the reflection and transmission of transient signals along the cable, influencing the overall system performance.

Correct Answer and Explanation
The correct answer to the question is option 'D' - 50 Ω. This surge impedance value indicates that the cable has a high impedance to surge currents, making it suitable for applications where protection against transient events is essential. By knowing the surge impedance of a cable, engineers can design effective protection measures and ensure the reliability of the power system.

Explanation:
The surge impedance of a cable is given by the formula:
\[ Z_s = \sqrt{L/C} \]
Where:
- \( Z_s \) = Surge Impedance
- \( L \) = Unit Inductance
- \( C \) = Unit Capacitance
Given that the unit inductance and unit impedance of the cable are both equal to 1, the surge impedance can be calculated as:
\[ Z_s = \sqrt{1/1} = 1 \, ohm \]
Therefore, the magnitude of the surge impedance for this cable is 1 ohm.

Incorrect Statement Explanation:

Shunt Capacitors:
- Shunt capacitors are used to improve power factor by supplying reactive power to the system.
- They are typically used for lagging power factor circuits to offset the inductive loads.
- The VAr (Reactive Volt-Ampere) produced by the shunt capacitors increases as the voltage drops, not drops as mentioned in the incorrect statement.
- Shunt capacitors help maintain the voltage value by supplying reactive power.

Variable Impedance Type Loads:
- Shunt capacitors are not of variable impedance type loads. They are fixed capacitors designed to provide a specific amount of reactive power to the system.
- Variable impedance type loads are typically used to minimize losses and voltage drop in a system, but shunt capacitors serve a different purpose.
Therefore, option 'D' is incorrect as shunt capacitors are not of variable impedance type loads.

Connection of Resistance and Capacitance Parameters in Long Transmission Lines

In long transmission lines, the resistance and capacitance parameters of the lines are connected in shunt and parallel.

Explanation:

- A transmission line consists of conductors that carry electrical energy from one point to another. The conductors are usually made of copper or aluminum and are separated by an insulating material to prevent any short circuits.
- The resistance of a transmission line is the opposition it offers to the flow of electrical current. This resistance is due to the conductivity of the conductors and the frequency of the current.
- The capacitance of a transmission line is the ability of the conductors to store electrical charge. This capacitance is due to the proximity of the conductors and the frequency of the current.
- In long transmission lines, the resistance and capacitance parameters are connected in shunt and parallel. This means that the resistance and capacitance are connected between the two conductors of the transmission line.
- The shunt connection of resistance and capacitance parameters means that the resistance and capacitance are connected in parallel. In this configuration, the resistance and capacitance form a branch that is connected between the two conductors of the transmission line.
- The parallel connection of resistance and capacitance parameters means that the resistance and capacitance are connected in shunt. In this configuration, the resistance and capacitance form a branch that is connected in parallel with the transmission line.
- The shunt and parallel connection of resistance and capacitance parameters is necessary in long transmission lines to improve the efficiency and performance of the transmission line. This configuration helps to reduce the losses due to resistance and capacitance and improve the voltage and current levels in the transmission line.

Conclusion:

In summary, the resistance and capacitance parameters of long transmission lines are connected in shunt and parallel to improve the efficiency and performance of the transmission line. This configuration helps to reduce the losses due to resistance and capacitance and improve the voltage and current levels in the transmission line.

Understanding Hybrid Parameters
Hybrid parameters, or h-parameters, are used to characterize the behavior of linear electronic devices, particularly transistors in small-signal models. Among these parameters, h11 plays a crucial role.
What is h11?
- Definition: h11 is defined as the short circuit input impedance of a two-port network, typically a transistor.
- Significance: It represents how much input impedance the device presents when the output is shorted, providing insights into the device's input characteristics.
Why is h11 the Correct Answer?
- Short Circuit Condition: The term "short circuit" indicates that the output is connected directly to ground (zero voltage), allowing us to measure how the input behaves under this condition.
- Impedance Measurement: When the output is shorted, the input impedance can be determined by applying a small signal voltage and measuring the resulting input current.
Other Hybrid Parameters for Comparison
- h21 (Short Circuit Forward Current Gain): This measures the current gain from input to output when the output is shorted.
- h12 (Open Circuit Reverse Voltage Gain): This parameter indicates the voltage gain from output to input when the input is open-circuited.
- h22 (Open Circuit Output Admittance): This describes the output admittance when the input is left open.
Conclusion
In summary, h11 is specifically the short circuit input impedance. Understanding this parameter is vital in analyzing and designing amplifier circuits, ensuring optimal performance for electronic devices.

Introduction:
Capacitors with automatic power factor controller are commonly used in plants to improve power factor and reduce reactive power demand. They help in optimizing the power consumption and minimizing penalties associated with low power factor.

Explanation:
a) Increase the load current of the plant:
Capacitors with automatic power factor controller do not increase the load current of the plant. In fact, they help in reducing the load current by compensating for the reactive power and improving the power factor.

b) Reduce active power drawn from the grid:
Capacitors with automatic power factor controller help in reducing the active power drawn from the grid. They compensate for the reactive power, which in turn reduces the total power demand from the grid. This leads to a more efficient use of electrical energy and lower electricity bills.

c) Reduce the voltage of the plant:
Capacitors with automatic power factor controller do not reduce the voltage of the plant. They help in maintaining a stable voltage level by compensating for the reactive power and improving the power factor. This ensures that the electrical equipment in the plant operates within the desired voltage range.

d) Reduce the reactive power drawn from the grid:
The correct answer is option 'd'. Capacitors with automatic power factor controller help in reducing the reactive power drawn from the grid. They provide reactive power locally, which compensates for the reactive power demand of the plant. This reduces the burden on the grid and improves the overall power factor of the plant.

Benefits of using capacitors with automatic power factor controller:
- Improved power factor: Capacitors compensate for the lagging reactive power, which results in an improved power factor. This helps in reducing losses in the electrical system and increases the overall efficiency.
- Reduced electricity bills: By reducing the reactive power demand and improving the power factor, capacitors help in reducing the total power consumption. This leads to lower electricity bills for the plant.
- Increased system capacity: By reducing the reactive power demand, capacitors free up the capacity of the electrical system. This allows for the addition of more load without overloading the system.
- Reduced voltage drops: Capacitors help in maintaining a stable voltage level by compensating for the reactive power. This reduces voltage drops and ensures that the electrical equipment operates within the desired voltage range.
- Compliance with utility regulations: Many utility companies impose penalties for low power factor. By installing capacitors with automatic power factor controller, the plant can avoid these penalties and maintain compliance with utility regulations.

Conclusion:
Capacitors with automatic power factor controller are beneficial for plants as they help in reducing the reactive power demand, improving the power factor, and optimizing the power consumption. They do not increase the load current, reduce the voltage, or increase the active power drawn from the grid.

Operating Voltage Range for Medium Transmission Lines

Medium transmission lines are used for transmitting power over short to medium distances. The correct operating voltage range for medium transmission lines is more than 20 KV.

Reasoning

- Transmission lines are classified based on the voltage level they operate on.
- Medium transmission lines are used for transmitting power over short to medium distances, typically ranging from 20 KV to 400 KV.
- The correct operating voltage range for medium transmission lines is more than 20 KV. This means that the voltage level can be 20 KV or higher.

Conclusion

The correct operating voltage range for medium transmission lines is more than 20 KV. This is because medium transmission lines are used for transmitting power over short to medium distances, typically ranging from 20 KV to 400 KV.

Understanding AVR: Automatic Voltage Regulator
The term AVR stands for Automatic Voltage Regulator, a crucial component in electrical engineering, particularly in power systems. Here’s why option 'C' is the correct answer:
Purpose of AVR
- Voltage Regulation: The primary function of an AVR is to maintain a constant voltage level within a power system, ensuring that electrical devices operate efficiently and safely.
- Automatic Adjustment: It automatically adjusts the output voltage by controlling the excitation of the generator or adjusting transformer taps based on the load demand and voltage levels.
How AVR Works
- Feedback Mechanism: An AVR uses a feedback loop to monitor the output voltage. If the voltage deviates from the set point, the AVR makes real-time adjustments to restore the voltage to the desired level.
- Components Involved: Typically, an AVR consists of a voltage sensing circuit, a control circuit, and an output stage that regulates the excitation of the generator.
Importance of AVR in Electrical Systems
- Stability: AVRs play a vital role in preventing voltage fluctuations, which can harm electrical equipment and affect system stability.
- Protection: By maintaining a consistent voltage level, AVRs help protect sensitive electronic devices from damage due to overvoltage or undervoltage conditions.
Conclusion
In summary, the Automatic Voltage Regulator (AVR) is essential for maintaining voltage stability in electrical systems. Its ability to automatically adjust voltage levels makes it a key component in ensuring the smooth operation of power generation and distribution systems. Thus, the correct answer to the question is option 'C'.

The Nature of Power Factor when Surge Impedance Loading is Less than Load

When considering the nature of power factor in electrical systems, it is important to understand the concept of surge impedance loading (SIL). SIL is a measure of how much power a transmission line can carry, and it is determined by the line's electrical characteristics, such as its resistance, inductance, and capacitance. The surge impedance loading is typically expressed as a fraction of the line's surge impedance, which is the characteristic impedance of the line.

In the given scenario, the surge impedance loading is less than the load. This means that the power being drawn by the load is greater than what the transmission line can handle based on its surge impedance. In such a situation, the power factor is said to be lagging.

Explanation:
- Surge Impedance Loading (SIL): Surge impedance loading is the maximum power that can be transferred through a transmission line without causing excessive voltage drop or distortion. It is a measure of the line's ability to carry power and is determined by its electrical characteristics.
- Power Factor: Power factor is a measure of how effectively electrical power is being used in a system. It is the ratio of real power (watts) to apparent power (volt-amperes). Power factor is typically expressed as a value between 0 and 1, where 1 represents perfect power factor (unity), and values less than 1 indicate a lagging power factor.
- Lagging Power Factor: A lagging power factor occurs when the load in an electrical system causes the current to lag behind the voltage waveform. This is typically the case in systems with inductive loads, such as motors and transformers. Inductive loads require reactive power, which causes the current to lag behind the voltage.
- Surge Impedance Loading < /> When the surge impedance loading is less than the load, it means that the power being drawn by the load exceeds the maximum power that the transmission line can handle based on its surge impedance. This indicates that the line is being operated at a higher capacity than it is designed for, leading to increased losses and potential voltage drop.
- Conclusion: In the given scenario, where the surge impedance loading is less than the load, the power factor is lagging. This means that the current being drawn by the load lags behind the voltage waveform, indicating the presence of inductive components in the load.

Explanation:
To find the value of Zc, we need to analyze the conditions given in the problem statement.

Surge Impedance:
Surge impedance is the characteristic impedance of a transmission line, which is defined as the ratio of voltage to current for a traveling wave on the line. In this case, the surge impedance of the overhead line is given as 400 ohms.

No Reflection at the Junction:
According to the problem statement, there is no reflection at the junction where the overhead line is terminated with the cable. This implies that there is no impedance mismatch between the line and the cable, resulting in no reflected waves.

Implication:
When there is no reflection at the junction, it means that the impedance of the cable (Zc) must be equal to the surge impedance of the overhead line (400 ohms). This is because for a traveling wave to pass through the junction without any reflection, the impedances on both sides of the junction must match.

Answer:
Since the surge impedance of the overhead line is given as 400 ohms and there is no reflection at the junction, the value of Zc (impedance of the cable) must also be 400 ohms.

Therefore, the correct answer is option 'D' - None of these.

Summary:
In this problem, we analyzed the conditions given in the problem statement, including the surge impedance of the overhead line and the absence of reflection at the junction. By applying the concept of impedance matching, we concluded that the impedance of the cable must be equal to the surge impedance of the overhead line. Hence, the correct answer is none of the given options.

Shunt capacitance is neglected in the analysis of short transmission lines. This is because the shunt capacitance is relatively small in short lines as compared to its resistance and inductance. Therefore, it can be assumed that the line is purely resistive and inductive.

Explanation:
Shunt capacitance is the capacitance between the line conductors and the ground or between the conductors themselves. It is represented by a capacitor in the equivalent circuit of a transmission line. Shunt capacitance causes the current to flow from the line conductors to the ground or between conductors, resulting in a capacitive reactance. This reactance decreases the power-carrying capacity of the transmission line.

However, in the case of short transmission lines, the length of the line is small, usually less than 80 km. As a result, the shunt capacitance is small compared to the resistance and inductance of the line. Therefore, the capacitive reactance is negligible, and it can be assumed that the line is purely resistive and inductive.

In the analysis of long and medium transmission lines, the shunt capacitance cannot be neglected. In these cases, the length of the line is significant, resulting in a substantial shunt capacitance. Shunt capacitance causes a capacitive reactance, which significantly affects the line's performance, leading to voltage drop and power loss. Therefore, the shunt capacitance must be taken into account while analyzing long and medium transmission lines.

Conclusion:
Shunt capacitance is negligible in short transmission lines, and it can be assumed that the line is purely resistive and inductive. In contrast, shunt capacitance cannot be neglected in the analysis of long and medium transmission lines as it significantly affects the line's performance.

Voltagesc)Conductor spaced)Type of insulating materiale)All of the above.

Explanation:

Short Circuit Forward Current Gain (h21)

- The hybrid parameter h21, also known as short circuit forward current gain, is a key parameter in the analysis of a transistor's behavior.
- It represents the change in collector current with respect to the change in base current when the collector-emitter junction is short-circuited.
- This parameter is crucial in determining the amplification capabilities of a transistor in its active region.
- A higher value of h21 indicates a higher current gain and better amplification properties of the transistor.
- It is an essential parameter in designing and analyzing transistor circuits for various applications in electronics.

Therefore, the correct answer is short circuit forward current gain (c) for the hybrid parameter h21.

Introduction:
In medium transmission lines, the charging current flowing to earth refers to the current that flows between the conductors and the earth due to the capacitance between the conductors and the ground. This charging current is influenced by the capacitance of the transmission line and the voltage applied.

Explanation:
1. Charging Current:
- When a transmission line is energized, a voltage is applied across its conductors. This voltage creates an electric field between the conductors and the ground, leading to the formation of capacitance.
- The capacitance between the conductors and the ground allows a small amount of current to flow, known as the charging current. This current flows to or from the earth depending on the phase relationship between the voltage and the ground.

2. Magnitude of Charging Current:
- The magnitude of the charging current depends on the capacitance of the transmission line and the voltage applied.
- In medium transmission lines, the capacitance per unit length is relatively low compared to long transmission lines, resulting in a lower charging current.
- The charging current is also influenced by the line voltage. Higher voltages result in higher charging currents, while lower voltages result in lower charging currents.

3. Very High Charging Current:
- Very high charging currents typically occur in long transmission lines, where the capacitance per unit length is relatively high.
- In such cases, the charging current can be significant and may require compensation or grounding measures to control it.

4. Negligible Charging Current:
- Negligible charging currents occur in short transmission lines or when the conductor-to-ground capacitance is very low.
- In these scenarios, the charging current is so small that it can be considered insignificant and can be neglected.

Conclusion:
In medium transmission lines, the value of the charging current flowing to earth is considered medium. This is because the capacitance per unit length is relatively lower compared to long transmission lines, resulting in a lower charging current. Additionally, the voltage applied also influences the magnitude of the charging current.

Ferranti effect is a phenomenon that occurs in long transmission lines with high voltage and low power factor. It results in an increase in the receiving end voltage compared to the sending end voltage. This can lead to overvoltage conditions and potential damage to the equipment connected to the transmission line. To mitigate the Ferranti effect, current limiting reactors can be used.

Current Limiting Reactors
- Current limiting reactors are inductive devices that are connected in series with the transmission line. They limit the flow of current in the transmission line, thereby reducing the voltage at the receiving end.
- These reactors have a high inductance and are designed to have low resistance. This allows them to limit the flow of current while minimizing the power losses in the system.
- By limiting the current, the voltage drop along the transmission line is reduced, which helps in reducing the voltage at the receiving end.
- The current limiting reactors also help in improving the power factor of the system by reducing the reactive power flow. This further contributes to reducing the voltage at the receiving end and mitigating the Ferranti effect.

Other Options
- Relays: Relays are control devices that are used to monitor and control the operation of electrical equipment. They do not directly affect the Ferranti effect.
- Circuit Breakers: Circuit breakers are protective devices that are used to interrupt the flow of current in case of a fault or overload condition. They do not directly affect the Ferranti effect.
- Resistors: Resistors are passive devices that oppose the flow of current. While they can be used to limit the current, they may not be as effective as current limiting reactors in mitigating the Ferranti effect.

In conclusion, current limiting reactors are the most effective equipment for reducing the Ferranti effect in long transmission lines. They limit the flow of current, reduce the voltage drop along the line, and improve the power factor of the system.

**Explanation:**

Operating transmission lines close to their maximum power transfer capability can impair stability due to various factors. Let's explore these factors in detail:

**1. Voltage Stability:**
When transmission lines are operated near their maximum power transfer capability, the voltage at the receiving end of the line may drop significantly. This drop in voltage can lead to voltage instability, causing voltage collapse or even voltage instability in the entire power system. Voltage instability can result in voltage sags, flickering lights, and potential blackouts.

**2. Transient Stability:**
Transient stability refers to the ability of the power system to maintain synchronism after a disturbance. Operating transmission lines close to their maximum power transfer capability can reduce the margin of stability, making the system more susceptible to disturbances and reducing the ability to recover from them. This can lead to cascading failures and blackouts in the power system.

**3. Oscillatory Stability:**
Oscillatory stability refers to the ability of the power system to maintain stable oscillations after a disturbance. Operating transmission lines close to their maximum power transfer capability can reduce the damping of oscillations, leading to increased oscillatory instability. This can result in sustained oscillations, voltage fluctuations, and potential system instability.

**4. Control and Protection Issues:**
Operating transmission lines close to their maximum power transfer capability can also create control and protection issues. The protective relays may have a shorter operating time, resulting in slower fault clearance. This delay in fault clearance can lead to increased fault durations, potential equipment damage, and system instability.

**5. Voltage Regulation:**
Operating transmission lines close to their maximum power transfer capability can also affect the voltage profile of the power system. Voltage regulation becomes challenging as the transmission lines approach their maximum power transfer capability. Voltage drops along the transmission lines can result in inadequate voltage levels at load centers, affecting the efficient operation of electrical equipment and causing voltage stability issues.

**Conclusion:**
In conclusion, operating transmission lines close to their maximum power transfer capability can impair stability in the power system. It can lead to voltage instability, transient instability, oscillatory instability, control and protection issues, and voltage regulation challenges. Therefore, it is essential to operate transmission lines within their safe operating limits to ensure the stability and reliability of the power system.

The equivalent circuit of a medium transmission line is an RLC circuit in pie form.



The transmission line is a long conductor used for transmitting electrical power or signals from one point to another. A medium transmission line is a transmission line with moderate length, typically between 80 km and 250 km.

To represent the behavior of a medium transmission line, an equivalent circuit is used. This equivalent circuit consists of lumped elements that represent the electrical characteristics of the transmission line.



A series RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. In this circuit, the resistor represents the resistance of the transmission line, the inductor represents the inductance of the transmission line, and the capacitor represents the capacitance of the transmission line.

However, a series RLC circuit does not accurately represent the behavior of a medium transmission line because it does not take into account the distributed parameters of the transmission line, such as the distributed resistance, inductance, and capacitance.



A series RL circuit consists of a resistor (R) and an inductor (L) connected in series. This circuit also does not accurately represent the behavior of a medium transmission line because it does not consider the distributed capacitance of the transmission line.



A parallel RL circuit consists of a resistor (R) and an inductor (L) connected in parallel. This circuit also does not accurately represent the behavior of a medium transmission line because it does not take into account the distributed resistance and capacitance of the transmission line.



The RLC circuit in pie form is the most accurate representation of the behavior of a medium transmission line. It consists of a resistor (R), an inductor (L), and a capacitor (C) connected in a specific configuration.

In the RLC circuit in pie form, the resistor represents the distributed resistance of the transmission line, the inductor represents the distributed inductance of the transmission line, and the capacitor represents the distributed capacitance of the transmission line.

This circuit accurately models the propagation characteristics of a medium transmission line, including the effects of attenuation, distortion, and reflection.

Therefore, the equivalent circuit of a medium transmission line is an RLC circuit in pie form.

Surge Impedance Value of Overhead Lines
The surge impedance value of overhead lines is typically in the range of 400 to 600 ohms.

Explanation:
- What is Surge Impedance: Surge impedance is the characteristic impedance of a transmission line when it is excited by a surge or transient signal.
- Importance: Surge impedance is crucial in understanding the behavior of transmission lines during transient events such as lightning strikes or switching operations.
- Range for Overhead Lines: The surge impedance value for overhead lines falls in the range of 400 to 600 ohms. This range is determined by the physical characteristics of the overhead conductors and the surrounding environment.
- Factors Affecting Surge Impedance: The surge impedance of overhead lines is influenced by factors such as conductor spacing, line length, and the dielectric properties of the surrounding medium.
- Significance: Understanding the surge impedance value helps in designing protection systems for overhead lines to mitigate the effects of transient events and ensure the reliability of the power transmission network.
In conclusion, the surge impedance value of overhead lines plays a vital role in ensuring the proper functioning and protection of the power transmission system, with a typical range of 400 to 600 ohms for overhead lines.

Explanation:
Induction generators are not used for voltage control.

Tap changing transformer:
A tap changing transformer is a type of transformer that allows for voltage control by changing the number of turns in the primary or secondary winding. This allows for the adjustment of the voltage level to compensate for variations in the system voltage.

Series compensators:
Series compensators are devices that are used to improve the voltage stability and control in power systems. They are typically installed in series with a transmission line and can be used to adjust the voltage level and compensate for voltage drops or rises.

Synchronous phase modifiers:
Synchronous phase modifiers, also known as synchronous condensers, are devices that are used to control the voltage and reactive power in a power system. They are essentially synchronous machines that can operate either as generators or as motors, depending on the need for reactive power compensation.

Induction generators:
Induction generators are not typically used for voltage control. They are primarily used for power generation and are commonly used in wind turbines. Induction generators operate at a fixed speed and do not have the ability to actively control the voltage level.

Conclusion:
Of the given options, induction generators are not used for voltage control. Tap changing transformers, series compensators, and synchronous phase modifiers are all used for voltage control in power systems.

B) 50