Power Systems - Fundamentals of Power System & Power Transmission Complete Study Notes

Introduction to power plants

Bulk electric power is produced by special plants known as generating stations or power plants. A generating station essentially employs a prime mover coupled to an alternator for the production of electric power. The prime mover (e.g., steam turbine, water turbine etc.) converts energy from some other form into mechanical energy. The alternator converts mechanical energy of the prime mover into electrical energy. The electrical energy produced by the generating station is transmitted and distributed with the help of conductors to various consumers.

Depending upon the form of energy converted into electrical, the generating stations are classified as under:

Steam Power Station (Thermal Station):

A generating station which converts heat energy of coal combustion into electrical energy is known as a steam power station. A steam power station basically works on the Rankine cycle. Steam is produced in the roller by utilising the heat of coal combustion. The steam is then expanded in the prime mover (i.e., steam turbine) and is condensed in a condenser to be fed into the boiler again. The steam turbine drives the alternator which converts mechanical energy of the turbine into electrical energy.

This type of power station is suitable where coal and water are available in abundance and a large amount of electric power is to be generated.

Advantages:

1. The fuel (i.e., coal) used is quite cheap.
2. Less initial cost as compared to other generating stations.
3. It can be installed at any place irrespective of the existence of coal. The coal can be transported to the site of the plant by rail or road.
4. It requires less space as compared to the hydroelectric power station.
5. The cost of generation is lesser than that of the diesel power station

Disadvantages:

1. It pollutes the atmosphere due to the production of large amount of smoke and fumes.
2. It is costlier in running cost as compared to hydroelectric plant.

The schematic diagram for the steam power plant is shown in figure below:

 Hydro-electric Power Station:

A generating station which utilizes the potential energy of water at a high level for the generation of electrical energy is known as a hydro-electric power station.

Hydro-electricity power stations are generally located in hilly areas where dams can be built conveniently, and large water reservoirs can be obtained.

In a hydro-electric power station, water head is created by constructing a dam across a river or lake. From the dam, water is led to a water turbine. The water turbine captures the energy in the falling water and changes the hydraulic energy (i.e., product of head and flow of water) in to mechanical energy at the turbine shaft. The turbine drives the alternator which converts mechanical energy into electrical energy.

Advantages:

1. It requires no fuel as water is used for the generation of electrical energy.
2. It is quite neat and clean as no smoke or ash is produced.
3. It requires very small running charges because water is the source of energy which is available free of cost.
4. It is comparatively simple in construction and requires less maintenance.
5. It does not require along starting time like as team power station.
6. It is robust and has a longer life.
7. They also help in irrigation and controlling floods.

Disadvantages:

1. It involves high capital cost due to construction of dam.
2. There is uncertainty about the availability of huge amount of water due to dependence on weather condition.
3. It requires high cost of transmission lines as the plants is located in hilly areas which are quite away from the consumers.

  Nuclear Power Station:

A generating station in which nuclear energy is converted into electrical energy is known as a nuclear power station. In nuclear power station, heavy elements such as Uranium (U²³⁵) or Thorium (Th²³²) are subjected to nuclear fission in a special apparatus known as a reactor. The heat energy thus released is utilised in raising steam high temperature and pressure. The steam runs the steam turbine which converts steam energy into mechanical energy. The turbine drives the alternator which converts mechanical energy into electrical energy.

The most important feature of a nuclear power station is that huge amount of electrical energy can be produced from a relatively small amount of nuclear fuel as compared to other conventional types of power stations.

It has been found that complete fission of 1 kg of Uranium (U²³⁵) can produce as much energy as can be produced by the burning of 4,500 tons of high-grade coal.

Advantages:

1. The amount of fuel required quite small. Therefore, there is a considerable saving in the cost of fuel transportation.
2. A nuclear power plant requires less space as compared to any other type of the same size.
3. It has low running charges as a small amount of fuel is used for producing bulk electrical energy.
4. This type of plant is very economical for producing bulk electric power.
5. It can be located near the load centres because it does not require large quantities of water and need not be near coal mines. Therefore, the cost of primary distribution is reduced.
6. There are large deposits of nuclear fuels available all over the word Therefore, such plants Can ensure continued supply of electrical energy for thousands of years.
7. It ensures reliability of operation.

Disadvantages:

1. The fuel used is expensive and is difficult to recover.
2. The capital cost on a nuclear plants very high as compared to other types of plants.
3. The erection and commissioning of the plant requires greater technical knowledge.
4. The fission by-products are generally radioactive and may came a dangerous amount of radioactive pollution.
5. Maintenance charges are high due to lack of standardization.
6. Nuclear power plants are not well suited for varying loads as the reactor does not respond to the load fluctuation efficiently.
7. The disposal of the by-products, which are radioactive, is a big problem. They have either to be disposed off in a deep trench or in a sea away from seashore.

Introduction to transmission line

Transmission lines are the most essential part of power transmission systems. Transmission of bulk power can be accomplished either by alternating current (ac) or direct current (dc), using overhead lines, or underground cables. A transmission line is characterized by four parameters:

1. Series branch resistance
2. Series branch inductance
3. Shunt branch capacitance
4. Shunt branch conductance

The performance of the transmission line depends on these parameters.

The shunt capacitance increases with an increase in the magnitude of the operating voltage. The series resistance and the shunt conductance are the least important parameters as their effect on the transmission capacity is relatively very less. However, the series resistance completely determines the real power transmission  loss and hence, its presence must be considered. The shunt conductance accounts for the resistive leakage current. The leakage current mainly flows along the insulator strings and ionized pathways in the air, and changes with change in the weather, atmospheric humidity, pollution, and salt content. The effect of the shunt conductance under normal operating conditions is usually neglected.

  Inductance of a Conductor due to Internal Flux

Consider a current carrying conductor whose cross section is of a long cylindrical structure with radius ‘r’ metres and carrying a current ‘I’ Amperes as shown in figure below.

internal flux linkages Ψ_int is given by

inductance due to the internal flux is independent of the conductor dimensions and its given by

  Inductance of a Conductor due to External Flux

Consider a same conductor with cross section of a conductor be as radius ‘r’ metres and carrying a current ‘I’ Amperes is shown in figure below,

Consider two points A₁ and A₂ external to the conductor surface and at distances D₁ and D₂ respectively, from the centre of the conductor. The magnetic flux paths are concentric circles around the conductor. All the flux lines between A₁ and A₂ lie within the concentric cylindrical surfaces passing through A₁ and A₂. 

total flux Ψ₁₂ between A₁ and A₂ is

Therefore, the inductance due to the external flux linkages included between A₁ and A₂ is

 Inductance of a single-phase two wire system

Consider a single-phase circuit of two parallel conductors of radii r₁ and r₂ metres, separated by a distance ‘D’ metres, as shown in figure below, one conductor is the return circuit for the other.

The flux set up by the current in conductor 1 links it in the following ways:

1. The external flux set up by current I in conductor 1 at a distance equal to or greater than (D + r₂), that is, beyond conductor 2 from the centre of the conductor 1 does not link the circuit.
2. The external flux between r₁ and (D - r₂), that is, between conductors 1 and 2, links all the current I in conductor 1.
3. The external flux over the surface of conductor 2, that is, between (D – r₂) and (D + r₂) links a fraction of the current varying from I to zero.

In transmission lines, ‘D’ is much greater than r₁ and r₂; hence, it can be assumed that ‘D’ can be used instead of (D – r₂) or (D + r₂).

The inductance L₁ of the circuit due to current ‘I’ in conductor 1 is obtained by considering inductance due to internal flux linkages and the inductance due to external flux linkages with r₁ replacing D₁ and ‘D’ replacing D₂, we get

Now, in above equation, the term ¼ can be written as lne^1/4

Thus,

where r₁' = 0.7788r₁ is  the geometric mean radius (GMR) or the self-geometric mean distance (self-GMD) of a solid round conductor. GMR represents an infinitesimally thin-walled conductor of radius r₁'.

The current in conductor 2 flows in a direction opposite to that of conductor 1 , and the flux produced due to current in conductor 2, links the single-phase circuit in the same direction as that produced by conductor 1. Thus, the inductance due to current in conductor 2 is

Hence, the total inductance of the circuit taking r₁’ = r₂’ = r’ can be written as,

Inductance of stranded conductor

Stranded conductors are normally used for overhead transmission lines. Inductance of such conductors is calculated using the same relation as above. Consider a seven-strand cable as shown in figure below,

The self-GMD of a seven-strand cable is the 49^th root of 49 distances. If ‘r’ is the radius of each strand, then

Substituting values of various distances, we get,

Inductance of three-phase line

    Symmetrical Spacing

    Consider an arrangement of equilaterally spaced conductors in a three-phase circuit which is shown in figure below,

Each conductor has a radius ‘r’ metres and the spacing between the conductors is ‘D’ metres. Assume that the neutral wire is not present, hence, I_R + I_Y + I_B = 0.

Therefore, the flux linkages of the conductor ‘a’ is given as

Since, I_R = -(I_Y + I_B), given equation becomes,

Hence,

Unsymmetrical Spacing:

Consider an arrangement of conductors in a three-phase circuit (with unsymmetrical spacing) as shown in figure below,

Unsymmetrical spacing of the phase conductors of a three-phase line causes the flux linkages and inductance of each phase to be different and results in an unbalanced circuit.

The three phases can be balanced by exchanging 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 conductor positions is called transposition.

For a complete transmission cycle, the transposed lines are shown in figure below, where conductors are designated as R, Y, and B, and the positions occupied are numbered 1, 2, and 3, respectively.

The flux linkages of conductor R in position 1, when conductor Y is in position 2 and conductor B is in position 3, is given as

With conductor R in position 2, when conductor Y is in position 3 and conductor B is in position 1, the flux linkages is given as

Finally, with conductor R in position 3, when conductor Y is in position 1 and conductor B is in position 2, the flux linkages are

The average value of the flux linkages of conductor R is given as

The average inductance per phase, therefore, is given by

Inductance of Double circuit Line:

Practically, double circuit system is used for three-phase transmission lines on the same transmission tower so as to increase the reliability of power transmission. It is done so to have low value of mutual GMD, ‘D_m’ and high value of self- GMD, ‘D_s’ so that the inductance of the parallel lines has a low value and hence power transfer capability increases. Thus, the individual conductors of a phase should be spaced as widely as possible while the distances between phases are kept as low as permissible.

Consider an arrangement of conductors in a double circuit three phase transposed line as shown in figure below, keeping each phase at a different place i.e. Phase R in position 1 (a), Phase R in position 2 (b), and Phase R in position 3 (c).

The conductors R, Y, B belong to one circuit while conductors R’, Y’, B’ belong to another circuit.

The flux linkages Ψ_R1, Ψ_R2, Ψ_R3 of phase R in position 1, position 2, and position 3 respectively are

Inductance of bundled Conductors:

For EHV and UHV lines, bundled conductors having two or more conductors per phase are used. The use of bundled conductors reduces corona loss and decreases the reactance of the transmission line. The reduction of reactance results in increased GMR of the bundle.

Consider the following arrangements of bundles with two, three, and four conductors as shown in figure below:

Let D_s^b indicate the GMR of a bundled conductor, D_s the GMR of the individual conductors, and ‘d’ be the distance between adjacent conductors of a bundled conductor.

For a two-conductor bundle,

For a three-conductor bundle,

For a four-conductor bundle,

Introduction to distribution system

The part of power system which distributes electrical power to local consumer’s use is referred to as distribution system. In general, the distribution system is the electrical system between the sub-station fed by the transmission system and the consumers meters. It generally consists of distributors and the service mains.

Figure below shows the single line diagram of a typical low-tension distribution system:

  Feeders

A feeder is a conductor which connects the sub-station (or localised generating station) to the area where power is to be distributed. Generally, no tapping’s are taken from the feeder so that current in it remains the same throughout. The main consideration in the design of a feeder is the current carrying capacity.

  Distributor

A distributor is a conductor from which tapping’s are taken for supply to the consumers. Figure above, AB, BC, CD and DA are the distributors. The current through a distributor is not constant because tapping’s are taken at various places along its length. While designing a distributor, voltage drop along its length is the train consideration since the statutory limit of voltage variations is ±6% of rated value at the consumers’ terminals.

  Service mains

A service mains is generally a small cable which connects the distributor to the consumers’ terminals.

 Classification of distribution system

A distribution system may be classified according to

  Nature of current:

According to nature of current, distribution system may be classified as

(a) DC distribution system

(b) AC distribution system

Now-a-days, ac. system is universally adopted for distribution of electric power as it is simpler and more economical than direct current method.

  Type of construction:

According to type of construction, distribution system may be classified as

(a) overhead system

(b) underground system

The overhead system is generally employed for distribution as it is 5 to 10 times cheaper than the equivalent underground system. In general, the underground system is used at places where overhead construction is impracticable or prohibited by the local laws.

 Scheme of connection:

According to scheme of connection, the distribution system may be classified as

(a) radial system

(b) ring main system

(c) inter-connected system.

A.C. Distribution

Now-a-days electrical energy is generated, transmitted, and distributed in the form of alternating current. One important reason for the widespread use of AC in preference to DC is due to the fact that alternating voltage can be conveniently changed in magnitude by means of a transformer. Only, transformer has made it possible to transmit AC power at high voltages and utilise it at a safe potential. High transmission and distribution voltages have greatly reduced the current in the conductors and thus resulting in line losses.

The AC distribution system is classified into two categories:

(i) primary distribution system

(ii) secondary distribution system

(i) Primary distribution system: It is that part of a.c. distribution system which operates at voltages somewhat higher than general utilisation and handles large blocks of electrical energy than the average low-voltage consumer uses. The voltage used for primary distribution depends upon the amount of power to be conveyed and the distance of the substation required to be fed. The most commonly used primary distribution voltages are 11 kV, 6.6 kV and 3.3 kV. Due to economic considerations, primary distribution is earned out by 3- phase, 3-wire system.

Figure below shows a typical primary distribution system.

Electric power from the generating station is transmitted at high voltage to the substation located in or near the city. At this substation, voltage is stepped down to 11 kV with the help of step-down transformer. Power is supplied to various substations for distribution or to big consumers at this voltage. This forms the high voltage distribution or primary distribution.

(ii) Secondary distribution system: It is that part of AC distribution system which includes the range of voltages at which the ultimate consumer utilises the electrical energy delivered to them. The secondary distribution employs 400/230 V, 3-phase, 4-wire system.

Figure below shows a typical secondary distribution system.

D.C. Distribution

The Electrical power is almost exclusively generated, transmitted, and distributed as AC. However, for certain applications, DC supply is absolutely necessary.

DC supply is required for the operation of variable speed machinery (i.e., DC motors), for electromechanical work, for this purpose, AC power is converted into DC power at the substation by using converting machinery e.g., mercury arc rectifiers, rotary converters and motor-generator sets. The d.c. supply from the substation may be obtained in the form of

(i) 2-wire

(ii) 3-wire

(i) 2-wire DC System:

As the name implies, this system of distribution consists of two wires. One is the outgoing or positive wire and the other is the return or negative wire. The loads such as lamps, motors etc. are connected in parallel between the two wires. This system is never used for transmission purposes due to low efficiency but may be employed for distribution of DC Power.

(ii) 3-wire DC System:

It consists of two outers and a middle or neutral wire which is earthed at the substation. The voltage between the outers is twice the voltage between either outer, or neutral wire.

The principal advantage of this system is that it makes available two voltages at the consumer terminals, i.e., ‘V’ between any outer and the neutral and ‘2V’ between the outers. Loads requiring high voltage (e.g., motors) are connected across the outers, whereas lamps and heating circuits requiring less voltage are connected between outer and the neutral.

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