Study notes on Component of Power System For Electrical Engineering

By Yash Bansal|Updated : May 17th, 2021

In this article, you will find the study notes on Component of Power System which will cover the topics such as Line Conductor, Bundled Conductor, Insulator, Pin Type Insulator, Suspension Type Insulator, String Efficiency, Classification of Cable, Cable of 3-Phase Line, Dielectric Stress of Cable, Most Economical Size of Conductor, Grading of Cable, Capacitance Grading, Intersheath Grading, Line Parameter Calculation; Inductance & Capacitance Calculation, Classification of Transmission Line, Voltage Regulation.

In this article, you will find the study notes on Component of Power System which will cover the topics such as Line Conductor, Bundled Conductor, Insulator, Pin Type Insulator, Suspension Type Insulator, String Efficiency, Classification of Cable, Cable of 3-Phase Line, Dielectric Stress of Cable, Most Economical Size of Conductor, Grading of Cable, Capacitance Grading, Intersheath Grading, Line Parameter Calculation; Inductance & Capacitance Calculation, Classification of Transmission Line, Voltage Regulation.

Conductor

A conductor is a physical medium to carry electrical energy from one place to other. It is an important component of overhead and underground electrical transmission and distribution systems. The choice of a conductor depends on the cost and efficiency.

An ideal conductor has following features.

• It has maximum conductivity
• It has high tensile strength
• It has least specific gravity i.e. weight/unit volume
• It has least cost without sacrificing other factors.

Bundled Conductors

Bundle conductors are widely used for transmission line and have its own advantages and disadvantages. Bundle conductor is a conductor which consists several conductor cables which connected. Bundle conductors also will help to increase the current carried in the transmission line. The main disadvantage of Transmission line is it's having high wind load compare to other conductors

Insulators

The overhead line conductors should be supported on the poles or towers in such a way that currents from conductors do not flow to earth through supports i.e., line conductors must be properly insulated from supports. This is achieved by securing line conductors to supports with the help of insulators.

The insulators provide necessary insulation between line conductors and supports and thus prevent any leakage current from conductors to earth. In general, the insulators should have the following desirable properties

• High mechanical strength in order to withstand conductor load, wind load etc.
• The high electrical resistance of insulator material in order to avoid leakage currents to earth.
• The high relative permittivity of insulator material in order that dielectric strength is high.
• The insulator material should be non-porous, free from impurities and cracks otherwise the permittivity will be lowered.
• A high ratio of puncture strength to flashover.
• The most commonly used material for insulators of overhead line is porcelain but glass, steatite, and special composition materials are also used to a limited extent. Porcelain is produced by firing at a high temperature a mixture of kaolin, feldspar, and quartz. It is stronger mechanically than glass, gives less trouble from leakage and is less effected by changes in temperature.

Pin type insulators

As the name suggests, the pin type insulator is secured to the cross-arm on the pole. There is a groove on the upper end of the insulator for housing the conductor. The conductor passes through this groove and is bound by the annealed wire of the same material as the conductor Pin type insulators are used for transmission and distribution of electric power at voltages upto 33 kV. Beyond operating voltage of 33 kV, the pin type insulators become too bulky and hence uneconomical.

Suspension type insulators

The cost of pin type insulator increases rapidly as the working voltage is increased. Therefore, this type of insulator is not economical beyond 33 kV. For high voltages (>33 kV). They consist of a number of porcelain discs connected in series by metal links in the form of a string.

• Suspension type insulators are cheaper than pin type insulators for voltages beyond 33 kV.
• Each unit or disc of suspension type insulator is designed for low voltage, usually 11 kV. Depending upon the working voltage, the desired number of discs can be connected in series.
• If anyone disc is damaged, the whole string does not become useless because the damaged disc can be replaced by the sound one.
• The suspension arrangement provides greater flexibility to the line. The connection at the
cross arm is such that insulator string is free to swing in any direction and can take up the position where mechanical stresses are minimized.
• In case of increased demand on the transmission line, it is found more satisfactory to supply the greater demand by raising the line voltage than to provide another set of conductors. The additional insulation required for the raised voltage can be easily obtained in the suspension arrangement by adding the desired number of discs.

String Efficiency

The ratio of voltage across the whole string to the product of number of discs and the voltage across the disc nearest to the conductor is known as string efficiency i.e.,

where n = number of the disc in the string.

Classification of Cables:

Cables for underground service may be classified in two ways according to

(i) the type of insulating material used in their manufacture

(ii) the voltage for which they are manufactured.

However, the latter method of classification is generally preferred, according to which cables can be divided into the following groups:

• Low-tension (L.T.) cables — upto 1000 V
• High-tension (H.T.) cables — upto 11,000 V
• Super-tension (S.T.) cables — from 22 kV to 33 kV
• Extra high-tension (E.H.T.) cables — from 33 kV to 66 kV
• Extra Online Classroom Program voltage cables — beyond 132 kV

A cable may have one or more than one core depending upon the type of service for which it is intended. It may be (i) single-core (ii) two-core (iii) three-core (iv) four-core etc. For a 3-phase service, either 3-single-core cables or three-core cable can be used depending upon the operating voltage and load demand.

Cable for 3-phase

In practice, underground cables are generally required to deliver 3-phase power. For the purpose, either three-core cable or three single core cables may be used. For voltage upto 66 kV, 3-core cable (i.e., multi-core construction) is preferred due to economic reasons.

However, for voltages beyond 66 kV, 3-core-cables become too large and unwieldy and, therefore, single-core cables are used. The following types of cables are generally used for 3-phase service:

• Belted cables — upto 11 kV
• Screened cables — from 22 kV to 66 kV
• Pressure cables — beyond 66 kV

Dielectric Stress in Cable

The electric intensity at a point x meters from the center of the cable is

It is clear from the above equation that potential gradient varies inversely as the distance x. Therefore, the potential gradient will be maximum when x is minimum i.e. when x = d/2 or at the surface of the conductor. On the other hand, the potential gradient will be minimum at x = D/2 or at sheath surface.

Most Economical Size of Conductor:

For given values of V and D, the most economical conductor diameter will be one for which gmax has a minimum value. The value of gmax will be minimum when dln D/d is maximum i.e,

and the value of gmax under this condition is

gmax = 2V/d volt/meter

• The process of achieving uniform electrostatic stress in the dielectric of cables is known as grading of cables. It has already been shown that electrostatic stress in a single core cable has a maximum value (gmax) at the conductor surface and goes on decreasing as we move towards the sheath.
• The maximum voltage that can be safely applied to a cable depends upon gmax i.e., electrostatic stress at the conductor surface. For safe working of a cable having homogeneous dielectric, the strength of dielectric must be more than gmax.
• If a dielectric of high strength is used for a cable, it is used only near the conductor where stress is maximum. But as we move away from the conductor, the electrostatic stress decreases, so the dielectric will be unnecessarily over strong.

The following are the two main methods of grading of cables: (i) Capacitance grading (ii) Intersheath grading

The process of achieving uniformity in the dielectric stress by using layers of different dielectrics is known as capacitance grading.

In capacitance grading, the homogeneous dielectric is replaced by a composite dielectric. The composite dielectric consists of various layers of different dielectrics in such a manner that relative permittivity > r of any layer is inversely proportional to its distance from the center.

The capacitance grading can be explained as there are three dielectrics of outer diameter d1, d2, and D and of relative permittivity >1, >2 and >3 respectively. If the permittivity is such that >1 > 2 > 3 and the three dielectrics are worked at the same maximum stress, then

Total p.d. between core and the earthed sheath is

V = V1 + V2 + V3

In this method of cable grading, a homogeneous dielectric is used, but it is divided into various layers by placing metallic inters heaths between the core and lead sheath. The inter sheaths are held at suitable potentials which are in between the core potential and earth potential. This arrangement improves voltage distribution in the dielectric of the cable and consequently more uniform potential gradient is obtained.

Since the dielectric is homogeneous, the maximum stress in each layer is the same i.e.,
g1max = g2max = g3max = gmax

As the cable behaves like three capacitors in series, therefore, all the potentials are in phase i.e. Voltage between conductor and earthed lead sheath

V = V1 + V2 + V3

• There are complications in fixing the sheath potentials.
• The inter sheaths are likely to be damaged during transportation and installation which might result in local concentrations of potential gradient.
• There are considerable losses in the inter sheaths due to charging currents. For these reasons, inter sheath grading is rarely used.

TRANSMISSION LINE PARAMETER

Line Inductance: When an alternating current flows through a conductor, a changing flux is set up which links the conductor. Due to these flux linkages, the conductor possesses inductance.

where ψ = flux linkage in weber-turns

I = current in turns

Flux Linkages: As stated earlier, the inductance of a circuit is defined as the flux linkages per unit current. Therefore, in order to find the inductance of a circuit, the determination of flux linkages is of primary importance. We shall discuss two important cases of flux linkages.

Flux linkages due to internal flux

Flux linkages due to external flux. Now let us calculate the flux linkages of the conductor due to external flux.

Inductance of Single-Phase Two Wire Line

A single phase line consists of two parallel conductors which form a rectangular loop of one turn. When an alternating current flows through such a loop, a changing magnetic flux is set up. The changing flux links the loop and hence the loop possesses inductance.

Inductance of conductor A,

r′ = r e-1/4= 0·7788 r  called geometric mean radius (GMR) of the conductor.

Note that r′ = 0·7788 r is applicable to only solid round conductor.

Loop inductance = 2 LA = 2×2×10−7 log d/r′  -H/m

The figure shows the three conductors A, B, and C of a 3-phase line carrying currents IA, IB and IC respectively. Let d1, d2, and d3 be the spacing between the conductors as shown. Let us further assume that the loads are balanced i.e. IA + IB + IC = 0.

Flux linkages with conductor A due to its own current

Flux linkages with conductor A due to current I

Flux linkages with conductor A due to current I

The total flux linkage with the conductor A is

As IA+ IB+IC=0

Case1-Symmetrical Spacing: If the three conductors A, B, and C are placed symmetrically at the corners of an equilateral triangle of side d, then, d1 = d2 = d3 = d. Under such conditions

Case 2-Unsymmetrical spacing: When 3-phase line conductors are not equidistant from each other, the conductor spacing is said to be unsymmetrical. Under such conditions, the flux linkages and inductance of each phase are not the same.A different inductance in each phase results in unequal voltage drops in the three phases even if the currents in the conductors are balanced.

Note: In order that voltage drops are equal in all conductors, we generally interchange the positions of the conductors at regular intervals along the line so that each conductor occupies the original position of every other conductor over an equal distance. Such an exchange of positions is known as transposition.

Transposition of three-phase conductor

The phase conductors are designated as A, B and C and the positions occupied are numbered 1, 2 and 3. The effect of transposition is that each conductor has the same average inductance.

Capacitance of Single-Phase Two Wire Line

Consider a single phase overhead transmission line consisting of two parallel conductors A and B spaced d meters apart in the air. Suppose that radius of each conductor is r meters. Let their respective charge be + Q and − Q coulombs per meter length.

Capacitance to neutral: Above equation gives the capacitance between the conductors of a two-wire line. Often it is desired to know the capacitance between one of the conductors and a neutral point between them. Since the potential of the mid-point between the conductors is zero, the potential difference between each conductor and the ground or neutral is half the potential difference between the conductors.

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