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Electrical power can be transmitted using both overhead lines and underground cables.
Overhead transmission is widely used because it is economical and easier to inspect and maintain. Underground transmission is preferred where space, appearance, safety, or environmental conditions make overhead lines unsuitable.
⚡ Power transmission can be carried out through overhead lines as well as underground cables.
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A service main is the conductor that connects the distributor to the consumer's installation or terminals.
A feeder generally carries power from a substation to a distribution area, while a distributor has tapping points from which consumers are supplied.
⚡ Feeder → Substation to distribution area
⚡ Distributor → Consumer tapping points
⚡ Service main → Distributor to consumer
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A feeder normally carries current from a substation to a distribution area without intermediate consumer tapping. Therefore, its cross-sectional area is mainly selected according to its current-carrying capacity.
⚡ Feeder → Mainly designed based on current-carrying capacity.
⚡ Distributor → Mainly designed based on permissible voltage drop.
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A distributor supplies power to consumers at different tapping points. Therefore, maintaining the consumer voltage within permissible limits is very important. Hence, the distributor is primarily designed considering voltage drop.
⚡ Feeder → Current-carrying capacity.
⚡ Distributor → Voltage-drop consideration.
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A feeder normally carries power from a generating station, transmission substation, or distribution substation toward the distribution area. It generally has no consumer tapping along its length.
⚡ Feeder → No intermediate consumer tapping normally.
⚡ Distributor → Consumer tapping is provided.
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A distributor is a conductor from which various consumer connections or tapping points are taken. Its voltage drop is therefore an important design consideration.
⚡ Distributor = conductor having consumer tapping points.
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The radial distribution system has a simple arrangement in which power flows from one source toward the loads. Because of its simple construction and lower conductor requirements, its initial cost is generally the lowest.
Its major disadvantage is comparatively poor reliability because a fault can interrupt supply to downstream consumers.
⚡ Radial → Simple and economical, but lower reliability.
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An interconnected distribution system receives power from more than one source. If one source or section becomes unavailable, supply can often be maintained through another path.
⚡ Interconnected system → Highest reliability among the listed systems.
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In a radial system, each load is normally supplied through a single electrical path from the source. The arrangement resembles the branches of a tree.
⚡ Radial = One source + one main path toward loads.
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Since a radial system generally has only one path from the source to a consumer, a fault on that path can interrupt supply to downstream loads. Therefore, its major disadvantage is poor reliability.
⚡ Main advantage → Simple and economical.
⚡ Main disadvantage → Poor continuity/reliability.
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A ring-main system forms a closed electrical path around the distribution area. Supply can reach loads from alternative directions, improving continuity compared with a radial arrangement.
⚡ Ring-main → Closed loop and improved continuity of supply.
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The ring-main arrangement provides an alternative path for power flow. Consequently, a section can often be isolated during a fault while supply is maintained to other sections.
⚡ Ring-main → Better continuity than radial system.
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An interconnected distribution system is supplied from more than one source. This arrangement provides flexibility and improves reliability and continuity of supply.
⚡ Interconnected = Multiple supply sources.
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Ring-main systems provide alternative paths for current flow, making them suitable where continuity of supply is important.
⚡ Important continuity → Ring-main system.
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Consumers are required to receive voltage within an acceptable range. Excessive voltage drop along a distributor can result in inadequate voltage at distant consumers.
⚡ Distributor design is strongly influenced by permissible voltage drop.
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The basic components of a conventional distribution system include the feeder, distributor, and service main.
⚡ Distribution system → Feeder + Distributor + Service main.
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A feeder carries electrical power from a substation toward the distribution area. Consumer tapping is normally not provided along its length.
⚡ Substation → Feeder → Distribution area.
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In an ideal feeder with no intermediate consumer tapping, the same load current flows through the entire feeder. Hence its current is approximately constant along its length.
⚡ Feeder current → Approximately constant when there are no intermediate taps.
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Since consumer loads are connected at different points of a distributor, current changes as we move along its length. Current generally decreases toward the end as different loads are tapped off.
⚡ Distributor current → Varies along the length because of consumer tapping.
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The service main is the final connection between the distributor and the consumer installation.
⚡ Service main → Distributor to consumer.
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Underground distribution is generally preferred in densely populated areas because it improves appearance, reduces visual obstruction and can provide greater protection against accidental contact with live conductors.
⚡ Urban areas → Underground distribution is often preferred.
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Underground cables require excavation, ducts or cable trenches and specialized installation. Therefore, their initial installation cost is generally higher than that of overhead lines.
⚡ Underground → Better appearance but higher initial cost.
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Underground cables are not exposed on poles and towers. Consequently, there are fewer visible conductors and supporting structures, giving the installation a cleaner appearance.
⚡ Major visible advantage of underground system → Better appearance.
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Overhead systems can generally be extended more easily by adding poles, towers, conductors and associated equipment. They also normally have lower initial installation costs than underground systems.
⚡ Overhead → Economical and comparatively easy to extend.
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Overhead lines require poles or towers and adequate clearances. In densely populated cities, obtaining the required right-of-way can be difficult, and the visible structures can also create visual obstruction.
⚡ Urban overhead-line problem → Right-of-way and visual obstruction.
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Aluminium and its alloys are widely used because aluminium provides good electrical conductivity while having relatively low weight. This gives favourable electrical and mechanical characteristics for overhead lines.
⚡ Aluminium → Light weight + good conductivity.
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ACSR means Aluminium Conductor Steel Reinforced. It consists of aluminium strands around a steel core.
⚡ ACSR = Aluminium Conductor Steel Reinforced.
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The steel core of an ACSR conductor provides the required mechanical strength to withstand tension and mechanical loads such as wind and the weight of the conductor.
⚡ Aluminium → Main current-carrying material.
⚡ Steel core → Mechanical strength.
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Conventional ACSR consists of a central steel core surrounded by aluminium strands. Aluminium provides most of the electrical conductivity while steel provides mechanical strength.
⚡ ACSR outer strands → Aluminium.
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The steel core increases the tensile strength of the ACSR conductor, allowing it to withstand mechanical tension and sag-related requirements.
⚡ Steel core = Mechanical strength.
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An overhead conductor must withstand mechanical forces caused by its own weight, wind, temperature changes and other loading conditions. Therefore, high tensile strength is desirable.
⚡ Good conductor → High conductivity + adequate tensile strength.
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A transmission conductor should carry current efficiently, requiring high electrical conductivity. It must also withstand mechanical tension, requiring high tensile strength.
⚡ Electrical requirement → High conductivity.
⚡ Mechanical requirement → High tensile strength.
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Copper has high electrical conductivity and therefore offers low resistance for a given cross-sectional area. This is one of the principal reasons for its traditional use as a conductor.
⚡ Copper → Excellent electrical conductivity.
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Aluminium is considerably lighter than copper while still providing good electrical conductivity. Its favourable conductivity-to-weight ratio makes it very useful for overhead transmission lines.
⚡ Aluminium → Light weight + good conductivity.
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Galvanized steel is commonly used for overhead earth or shield wires because it offers good mechanical strength and corrosion resistance.
⚡ Earth wire → Protects the line and equipment from lightning-related effects.
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An overhead earth wire, also called a shield wire, is installed above the phase conductors to intercept lightning strokes and provide a path toward earth, thereby reducing the likelihood of direct lightning strikes on the phase conductors.
⚡ Earth/shield wire → Lightning protection.
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Overhead conductors may be supported by poles in distribution systems and by towers in transmission systems.
⚡ Distribution → Poles are commonly used.
⚡ Transmission → Towers are commonly used.
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Steel lattice towers provide high mechanical strength and are widely used for supporting high-voltage and extra-high-voltage transmission conductors.
⚡ Steel lattice towers → High-voltage transmission.
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RCC (Reinforced Cement Concrete) poles are commonly used in electrical distribution systems because they provide adequate mechanical strength and durability.
⚡ RCC poles → Commonly used in distribution networks.
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Poles and towers mechanically support the conductors and maintain the required electrical clearances from ground, structures and other conductors.
⚡ Pole/Tower → Mechanical support + required electrical clearance.
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An insulator electrically separates the conductor from its supporting structure while mechanically supporting the conductor.
⚡ Insulator → Electrical insulation + mechanical support.
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An overhead-line insulator must support the conductor mechanically while withstanding mechanical forces caused by conductor weight, wind and other loads. Hence, high mechanical strength is essential.
⚡ Insulator → High mechanical strength is essential.
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Dielectric strength is the ability of an insulating material to withstand electric stress without electrical breakdown. An overhead-line insulator therefore needs high dielectric strength.
⚡ Good insulator → High dielectric strength + high insulation resistance.
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Shackle insulators are commonly used in low-voltage and lower-voltage distribution applications, especially at bends and ends of distribution lines.
⚡ Shackle insulator → Commonly associated with lower-voltage distribution.
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Pin insulators are mounted on poles or cross-arms. The conductor is secured to the upper portion of the insulator while the insulator electrically separates the conductor from the supporting structure.
⚡ Pin insulator → Mounted on pole/cross-arm support.
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Suspension insulator strings are widely used on high-voltage transmission lines. Additional disc units can be added to increase the insulation level for higher voltages.
⚡ High voltage → Suspension insulator strings.
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At dead ends and locations where the line changes direction significantly, the conductor experiences considerable mechanical tension. Strain insulators are designed to withstand these mechanical forces.
⚡ Strain insulator → Dead ends, corners and locations with high conductor tension.
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A suspension insulator string is formed by connecting multiple individual insulating units mechanically in series. More units can be added when a higher system voltage requires a greater insulation level.
⚡ Suspension string = Multiple insulating units connected mechanically.
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String efficiency describes how uniformly the voltage is distributed across the individual units of a suspension insulator string. Due to stray capacitance, the voltage distribution is generally not uniform.
⚡ String efficiency → Suspension insulator strings.
⚡ Higher string efficiency → More uniform voltage distribution.
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Ideally, each unit of a suspension insulator string should withstand an equal share of the total voltage. Therefore, the voltage distribution should be uniform.
In an actual string, stray capacitance causes unequal voltage distribution, with the unit nearest the conductor generally experiencing the highest voltage stress.
⚡ Ideal voltage distribution → Uniform.
⚡ Actual string → Voltage distribution is unequal because of capacitance effects.
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In a practical suspension-insulator string, the voltage does not divide equally among all the insulator discs. Therefore, the voltage distribution is unequal.
The main reason is the presence of stray capacitance between the metal fittings of the insulator string and the tower or earth. These capacitances cause different units of the string to experience different voltage stresses.
The insulator unit nearest the conductor generally experiences the highest voltage stress.
Since the individual voltages \(V_1,V_2,\ldots,V_n\) are not equal, the voltage distribution is non-uniform.
- Practical insulator-string voltage distribution is unequal.
- Stray capacitance is the major reason.
- The conductor-side unit has the highest electrical stress.
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A suspension-insulator string consists of several disc units connected in series. Ideally, the total voltage would divide equally among the discs. However, in practice, each disc has capacitance not only to the adjacent disc but also to the tower and earth.
These additional capacitances are called stray or shunt capacitances. Because of them, the voltage distribution becomes non-uniform.
The unit nearest the conductor generally receives the largest portion of the total voltage.
- Unequal distribution → mainly due to stray capacitance.
- Highest stress → conductor-side disc.
- String efficiency measures how uniformly voltage is distributed.
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The voltage distribution across a practical suspension-insulator string is non-uniform because of stray capacitances.
The insulator disc nearest the high-voltage conductor is subjected to the greatest voltage. Hence, it experiences the highest electrical stress.
This is important because excessive electrical stress on one disc can cause premature insulation failure.
A perfectly uniform distribution would give a string efficiency of \(100\%\).
- Conductor-side disc → highest voltage stress.
- Tower-side disc → comparatively lower voltage stress.
- Non-uniform distribution reduces string efficiency.
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String efficiency is improved when the voltage is distributed more uniformly among the insulator units.
Grading arrangements such as capacitance grading and guard rings are used to control the electric field and improve voltage distribution.
As the maximum voltage across any individual disc is reduced, string efficiency increases.
- Better voltage distribution → higher string efficiency.
- Grading arrangements reduce voltage concentration.
- Guard rings are commonly used for voltage grading.
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Corona is a phenomenon associated with ionization of the air surrounding a high-voltage conductor when the electric field near the conductor becomes sufficiently high.
The strong electric field accelerates free electrons in the surrounding air. These electrons collide with air molecules and may produce further ionization.
When the electric field reaches a sufficiently high value, ionization begins and corona may appear.
- Corona → electrical discharge around a high-voltage conductor.
- It involves ionization of surrounding air.
- Corona is important in EHV transmission systems.
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Corona starts when the electric field at the conductor surface becomes sufficiently high to ionize the surrounding air.
The electric field is influenced by conductor radius, conductor spacing, voltage and atmospheric conditions.
A smaller conductor radius produces a higher surface electric field for the same operating voltage.
Therefore, increasing the effective conductor radius is an important method of reducing corona.
- High surface electric field promotes corona.
- Larger effective conductor radius reduces corona tendency.
- Bundled conductors increase effective radius.
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Corona is undesirable in high-voltage transmission systems because it produces several effects.
First, energy is consumed in maintaining the ionization process, causing corona power loss. Corona can also generate electromagnetic disturbances that produce radio interference.
In addition, corona can produce a characteristic hissing or crackling sound known as audible noise.
- Corona causes power loss.
- Corona may cause radio interference.
- Corona may produce audible noise.
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Corona depends on several physical and environmental factors.
Conductor size: A larger conductor has a larger effective radius and therefore a lower surface electric field.
Surface condition: Rough, dirty or irregular conductor surfaces can locally increase electric-field intensity.
Atmospheric conditions: Air density, pressure, temperature, rain, fog and humidity can influence corona.
- Conductor radius affects corona.
- Rough surfaces increase local electric-field concentration.
- Weather and atmospheric conditions influence corona.
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Increasing conductor diameter increases the conductor radius. Consequently, the electric-field intensity at the conductor surface decreases.
Therefore, the conductor requires a higher voltage before corona begins.
Hence, a larger radius means a lower surface electric field and a reduced tendency for corona formation.
- Diameter ↑ → radius ↑.
- Radius ↑ → surface electric field ↓.
- Therefore, corona tendency ↓.
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In EHV transmission systems, each phase may consist of two or more subconductors separated by spacers. This arrangement is called a bundled conductor.
The bundle behaves electrically like a conductor having a larger effective radius. This reduces the electric-field intensity at the surface and therefore reduces corona.
Bundling also improves the transmission characteristics of EHV lines.
- Bundling is particularly important in EHV transmission.
- It increases the effective conductor radius.
- Corona and associated losses are reduced.
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A bundled conductor is formed by using two or more separate subconductors for one electrical phase.
The subconductors are maintained at a fixed spacing using mechanical spacers.
For example, a phase may use two, three or four subconductors depending upon the voltage level and transmission requirements.
- Bundle conductor = multiple subconductors belonging to one phase.
- Spacers maintain the physical separation.
- Used extensively in EHV transmission.
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The main electrical advantage of bundled conductors is reduction of corona effects.
Multiple subconductors increase the effective radius of the phase conductor. The surface electric-field intensity therefore decreases.
As \(r_{\text{effective}}\) increases, corona loss decreases.
- Bundle → effective radius ↑.
- Surface electric field ↓.
- Corona loss ↓.
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An overhead conductor cannot be installed perfectly straight between two supports. A certain amount of downward curvature called sag is intentionally provided.
Sag allows the conductor to accommodate changes in length caused by temperature variation. It also prevents excessive mechanical tension from being transferred to towers and supports.
where \(w\) is conductor weight per unit length, \(L\) is span and \(T\) is horizontal tension.
- Sag is necessary for mechanical safety.
- Temperature rise increases conductor length.
- Proper sag prevents excessive tension.
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When the temperature of an overhead conductor rises, the conductor undergoes thermal expansion.
Here, \(\alpha\) is the coefficient of thermal expansion. The conductor becomes longer, resulting in greater downward sag.
Therefore:
- Temperature ↑ → conductor length ↑.
- Conductor length ↑ → sag generally ↑.
- High-temperature conditions must be considered during line design.
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A flexible conductor suspended between two supports under its own uniformly distributed weight assumes a curve called a catenary.
For practical transmission-line calculations where sag is small compared with the span, the catenary can be approximated by a parabola.
- Exact conductor curve → catenary.
- Small-sag approximation → parabolic curve.
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The exact curve of a conductor under uniformly distributed weight is a catenary. However, for normal overhead-line calculations, sag is usually small compared with the span.
Under this condition, the catenary can be approximated by a parabola.
where \(d\) is sag, \(w\) is conductor weight per unit length, \(L\) is span and \(T\) is horizontal tension.
- Exact curve → catenary.
- Small sag approximation → parabola.
- Parabolic sag formula → \(d=\frac{wL^2}{8T}\).
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Sag is the vertical distance between the level of the supports and the lowest point of the conductor.
For a level span, the lowest point occurs approximately at the centre of the span.
- Sag is a vertical distance.
- It is not the span length.
- It is usually measured from support level to the lowest conductor point.
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When the two supports are at the same level and the conductor loading is uniform, the conductor curve is symmetrical.
Therefore, the lowest point of the conductor occurs at the midpoint of the span.
- Level supports + uniform loading → lowest point at midpoint.
- Unequal support levels require a different sag analysis.
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For a level span with uniformly distributed conductor weight, parabolic sag is given by:
From this equation:
Therefore, when conductor tension \(T\) increases, sag decreases.
- Tension ↑ → sag ↓.
- Tension ↓ → sag ↑.
- Very high tension is undesirable because it increases mechanical stress.
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Although increasing conductor tension reduces sag, excessive tension is mechanically dangerous.
High tension increases the mechanical stress in the conductor and transfers greater forces to towers, poles, clamps and foundations.
where \(\sigma\) is tensile stress, \(T\) is tension and \(A\) is the conductor cross-sectional area.
Hence, conductor tension must be selected as a compromise between acceptable sag and acceptable mechanical stress.
- High tension → low sag.
- Excessive tension → high mechanical stress.
- Transmission-line design requires an optimum tension.
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The resistance of a uniform conductor is given by:
Therefore, resistance is directly proportional to length:
If the length doubles while all other parameters remain unchanged, the resistance also doubles.
- Length ↑ → resistance ↑.
- Area ↑ → resistance ↓.
- Resistivity depends on material and temperature.
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The resistance of a uniform conductor is:
where:
- \(R\) = resistance in ohms
- \(\rho\) = resistivity of material
- \(L\) = conductor length
- \(A\) = cross-sectional area
Thus, resistance increases with length and decreases with cross-sectional area.
- Basic formula: \(R=\rho L/A\).
- Unit of resistance → ohm \((\Omega)\).
- Unit of resistivity → \(\Omega\cdot m\).
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In the resistance equation:
\(\rho\) represents the resistivity of the conductor material.
Resistivity indicates how strongly a material opposes the flow of electric current.
- \(\rho\) → resistivity.
- Unit → \(\Omega\cdot m\).
- Low resistivity materials are good electrical conductors.
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From the fundamental resistance equation:
Resistance is inversely proportional to cross-sectional area:
Therefore, increasing conductor area decreases resistance.
- Conductor area ↑ → resistance ↓.
- Larger conductors can carry greater current.
- Large conductor size also helps reduce \(I^2R\) losses.
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For metallic conductors, resistance generally increases with temperature.
Here, \(R_0\) is resistance at reference temperature, \(\alpha\) is the temperature coefficient of resistance and \(T-T_0\) is the temperature rise.
Therefore, when conductor temperature increases, its resistance increases.
- Metal conductor: temperature ↑ → resistance ↑.
- Higher resistance results in higher \(I^2R\) loss for the same current.
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Current flowing through a transmission-line conductor produces a magnetic field around the conductor. The magnetic flux links with the conductor and produces inductance.
where \(L\) is inductance, \(\lambda\) is flux linkage and \(I\) is current.
Therefore, transmission-line inductance is fundamentally associated with magnetic flux produced by current.
- Current → magnetic field.
- Magnetic flux linkages → inductance.
- Inductance produces inductive reactance.
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Whenever there is a potential difference between conductors, an electric field exists between them. This causes the transmission line to possess capacitance.
Capacitance exists between phase conductors and also between conductors and earth.
where \(C\) is capacitance, \(Q\) is stored charge and \(V\) is potential difference.
- Inductance → magnetic field.
- Capacitance → electric field.
- Transmission-line capacitance depends strongly on conductor geometry and spacing.
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A practical transmission line has several electrical characteristics. The three principal parameters emphasized in basic transmission-line analysis are resistance, inductance and capacitance.
For a complete distributed-parameter model, shunt conductance \(G\) is also considered.
- Basic line parameters → \(R,L,C\).
- Complete distributed model → \(R,L,C,G\).
- Resistance causes real-power loss.
- Inductance and capacitance affect reactive behavior.
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A practical transmission line is modeled using four distributed parameters:
- R → series resistance per unit length
- L → series inductance per unit length
- C → shunt capacitance per unit length
- G → shunt conductance per unit length
These parameters are distributed continuously along the line rather than being concentrated at a single point.
- Four distributed parameters → R, L, C, G.
- Series parameters → \(R,L\).
- Shunt parameters → \(C,G\).
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In the distributed transmission-line model, \(R\) represents the conductor's series resistance per unit length.
The total resistance over a length \(L\) is obtained by multiplying the resistance per unit length by the line length.
- \(R\) → series resistance.
- \(L\) → series inductance.
- \(C\) → shunt capacitance.
- \(G\) → shunt conductance.
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For a three-phase transmission system:
Therefore:
For constant power and power factor, increasing voltage reduces line current.
Since copper loss is:
reducing current produces a large reduction in transmission losses.
- Transmission voltage ↑ → current ↓ for the same power.
- Current ↓ → \(I^2R\) loss ↓.
- This is the fundamental reason for high-voltage transmission.
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For a three-phase system:
Rearranging:
Thus, for constant \(P\) and \(\cos\phi\), current is inversely proportional to voltage.
- Voltage ↑ → current ↓.
- Voltage doubled → current becomes approximately half.
- Lower current means lower copper loss.
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The power dissipated in the resistance of a conductor is given by:
Therefore:
This quadratic relationship is why reducing transmission current is so effective in reducing power loss.
- Copper loss → \(I^2R\).
- Current doubles → loss becomes four times.
- Current halves → loss becomes one-fourth.
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Electrical power dissipated in a resistor is:
Since \(V=IR\):
Hence the transmission-line resistive loss is:
- Basic power formula → \(P=VI\).
- Resistive loss → \(I^2R\).
- Transmission losses are strongly affected by current.
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For constant transmitted power and constant power factor:
Therefore:
If voltage becomes \(2V\):
Hence, current becomes half.
- For constant power: \(I\propto1/V\).
- Voltage ×2 → current ÷2.
- This is why power is transmitted at high voltage.
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Initial loss:
New current:
Therefore:
Hence:
The loss becomes one-fourth of its original value.
- Loss varies as \(I^2\).
- Current half → loss one-fourth.
- Current double → loss four times.
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For a fixed amount of transmitted power:
Increasing voltage decreases current. Since transmission loss varies as \(I^2\), the reduction in current produces a much larger reduction in resistive loss.
- High voltage → low current.
- Low current → low \(I^2R\) loss.
- High-voltage transmission improves efficiency.
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Transmission efficiency indicates how much of the power supplied at the sending end is successfully delivered to the receiving end.
Since transmission losses are always present in a practical line:
Therefore, receiving-end power is normally less than sending-end power.
- Efficiency = useful output / input × 100.
- For transmission: \(\eta=P_R/P_S\times100\%\).
- Higher losses → lower efficiency.
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Transmission efficiency is defined as receiving-end active power divided by sending-end active power.
Also:
Therefore, the efficiency must normally be less than \(100\%\).
- \(P_R\) → receiving-end power.
- \(P_S\) → sending-end power.
- \(\eta=P_R/P_S\times100\%\).
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Voltage regulation describes the change in receiving-end voltage as the load changes, usually from no-load to full-load conditions while keeping the sending-end voltage constant.
The value depends upon the line impedance and load power factor.
- Voltage regulation concerns receiving-end voltage.
- It depends on line impedance and load conditions.
- Power factor strongly affects regulation.
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The Ferranti effect occurs mainly in long AC transmission lines when they are lightly loaded or unloaded.
The distributed capacitance of the line draws a charging current even when the load current is very small.
Due to the interaction between line capacitance and inductance, the receiving-end voltage can rise above the sending-end voltage.
- Ferranti effect → mainly long AC lines.
- Most noticeable at light/no load.
- Receiving voltage can exceed sending voltage.
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Ferranti effect is characterized by an increase in receiving-end voltage under light-load or no-load conditions on long AC lines.
The principal reason is the charging current associated with the distributed line capacitance.
The effect becomes more pronounced as the line becomes longer.
- Ferranti effect → \(V_R>V_S\).
- Associated with line capacitance.
- Strongest under light/no-load conditions.
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Transmission-line capacitance causes a charging current to flow even when the external load current is very small.
This charging current interacts with the line inductance and causes the receiving-end voltage to rise under light-load conditions.
- Ferranti effect → capacitance phenomenon.
- Charging current exists due to line capacitance.
- Longer line → greater capacitance effect.
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The capacitance of a transmission line increases with its length. Consequently, the charging current also increases.
where \(C'\) is capacitance per unit length and \(L\) is line length.
Therefore, long transmission lines experience a stronger Ferranti effect than short lines.
- Line length ↑ → total capacitance ↑.
- Capacitance ↑ → charging current ↑.
- Ferranti effect becomes more significant.
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For a short transmission line, the effect of shunt capacitance is relatively small and is commonly neglected in the basic model.
The line is then represented primarily by its series impedance:
Hence:
- Short line → shunt capacitance usually neglected.
- Series impedance is retained.
- Basic model → series \(R+jX\).
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In medium transmission lines, the effect of shunt capacitance becomes significant enough that it cannot normally be ignored.
Therefore, the equivalent circuit includes both the series impedance and shunt admittance.
Common models include the nominal-\(\pi\) and nominal-T models.
- Short line → capacitance usually neglected.
- Medium line → shunt capacitance considered using lumped models.
- Long line → distributed parameters are used.
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In a long transmission line, resistance, inductance, capacitance and conductance are distributed continuously along the entire length.
Therefore, a distributed-parameter model is used instead of treating all parameters as concentrated at one location.
The propagation constant and characteristic impedance are important quantities in long-line analysis.
- Long line → distributed parameters.
- Parameters → \(R,L,C,G\).
- Propagation constant → \(\gamma=\sqrt{Z'Y'}\).
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ABCD parameters, also called transmission parameters, provide a convenient relationship between sending-end and receiving-end quantities.
In matrix form:
- ABCD parameters → transmission parameters.
- They relate sending-end and receiving-end quantities.
- Basic equations: \(V_S=AV_R+BI_R\), \(I_S=CV_R+DI_R\).
📖 View Answer and Detailed Explanation
A transmission system transfers bulk electrical power from generating stations to major load centers and substations.
The overall electrical-power system can broadly be represented as:
Transmission lines are therefore an essential link between generation and distribution networks.
- Generation produces electrical power.
- Transmission transfers bulk power over longer distances.
- Distribution delivers power to consumers.
📖 View Answer and Detailed Explanation
Electrical power follows a structured path from the generating station to the final consumer.
At the generating station, electrical energy is produced. The generated voltage is then stepped up using a transformer for economical transmission.
The transmission network carries bulk power over long distances. Substations then reduce the voltage to appropriate distribution levels.
Finally, the distribution network delivers electrical power to individual consumers.
The reason for transmitting power at high voltage can be understood from the three-phase power equation:
For a fixed power:
Therefore, increasing the transmission voltage reduces the current. Since transmission loss is proportional to \(I^2R\), the reduction in current significantly reduces power losses.
- Generation → Transmission → Distribution → Consumer.
- Transmission carries bulk electrical power over long distances.
- High voltage reduces transmission current.
- Lower current reduces \(I^2R\) losses.
- Step-up transformers are used before long-distance transmission.
- Step-down transformers are used before distribution and utilization.