Pressurized Water Reactor (PWR)

Pressurized Water Reactor (PWR)

Pressurized water reactors (PWRs) (also VVER if of Russian design) are generation II nuclear power reactors that use ordinary water under high pressure as coolant and neutron moderator. The primary coolant loop is kept under high pressure to prevent the water from boiling, hence the name. PWRs are one of the most common types of reactors and are widely used all over the world. More than 230 of them are in use to generate electric power, and several hundred more for naval propulsion. They were originally designed by the Bettis Atomic Power Laboratory as a nuclear submarine power plant.The below diagram shows the PWR and its main parts.

1.Reactor vessel 2.Fuel elements 3.Control rods 4.Control rod drive 5.Pressurizer 6.Steam generator 7.Main circulating pump 8.Fresh steam 9.Feedwater 10.High pressure turbine 11.Low pressure turbine 12.Generator 13.Exciter 14.Condenser 15.Cooling water 16.Feedwater pump 17.Feedwater pre-heater 18.Concrete shield 19.Cooling water pump

The pressurized water reactor belongs to the light water type: the moderator and coolant are both light water (H2O). It can be seen in the figure that the cooling water circulates in two loops, which are fully seperated from one another.
The primary circuit water (dark blue) is continuously kept at a very high pressure and therefore it does not boil even at the high operating temperature. (Hence the name of the type.) Constant pressure is ensured with the aid of the pressurizer (expansion tank). (If pressure falls in the primary circuit, water in the pressurizers is heated up by electric heaters, thus raising the pressure. If pressure increases, colder cooling water is injected to the pressurizer. Since the upper part is steam, pressure will drop.) The primary circuit water transferes its heat to the secondary circuit water in the small tubes of the steam generator, it cooles down and returns to the reactor vessel at a lower temperature.
Since the secondary circuit pressure is much lower than that of the primary circuit, the secondary circuit water in the steam generator starts to boil (red). The steam goes from here to the turbine, which has high and low pressure stages. When steam leaves the turbine, it becomes liquid again in the condenser, from where it is pumped back to the steam generator after pre-heating.
Normally, primary and secondary circuit waters cannot mix. In this way it can be achieved that any potentially radioactive material that gets into the primary water should stay in the primary loop and cannot get into the turbine and condenser. This is a barrier to prevent radioactive contamination from getting out.
In pressurized water reactors the fuel is usually low (3 to 4 percent) enriched uranium oxide, sometimes uranium and plutonium oxide mixture (MOX). In today's PWRs the primary pressure is usually 120 to 160 bars, while the outlet temperature of coolant is 300 to 320 °C. PWR is the most widespread reactor type in the world: they give about 64% of the total power of the presently operating nuclear power plants.


Two things are characteristic for the pressurized water reactor (PWR) when compared with other reactor types:

• In a PWR, there are two separate coolant loops (primary and secondary), which are both filled with ordinary water (also called light water). A boiling water reactor, by contrast, has only one coolant loop, while more exotic designs such as breeder reactors use substances other than water (i.e., liquid metal as sodium) for the task.
• The pressure in the primary coolant loop is at typically 15-16 Megapascal, notably higher than in other nuclear reactors. As an effect of this, the gas laws guarantee that only sub-cooled boiling will occur in the primary loop. By contrast, in a boiling water reactor the primary coolant is allowed to boil and it feeds the turbine directly without the use of a secondary loop.

Coolant

Ordinary water is used as primary coolant in a PWR and flows through the reactor at a temperature of roughly 315 °C (600 °F). The water remains liquid despite the high temperature due to the high pressure in the primary coolant loop (usually around 2200 psig [15 MPa, 150 atm]). The primary coolant loop is used to heat water in a secondary circuit that becomes saturated steam (in most designs 900 psia [6.2 MPa, 60 atm], 275 °C [530 °F]) for use in the steam turbine.

Moderator

Pressurized water reactors, like thermal reactor designs, require the fast fission neutrons in the reactor to be slowed down (a process called moderation) in order to sustain its chain reaction. In PWRs the coolant water is used as a moderator by letting the neutrons undergo multiple collisions with light hydrogen atoms in the water, losing speed in the process. This "moderating" of neutrons will happen more often when the water is more dense (more collisions will occur). The use of water as a moderator is an important safety feature of PWRs, as any increase in temperature causes the water to expand and become less dense; thereby reducing the extent to which neutrons are slowed down and hence reducing the reactivity in the reactor. Therefore, if reactor activity increases beyond normal, the reduced moderation of neutrons will cause the chain reaction to slow down, producing less heat. This property, known as the negative temperature coefficient of reactivity, makes PWR reactors very stable.

Fuel

The uranium used in PWR fuel is usually enriched several percent in 235U. After enrichment the uranium dioxide (UO2) powder is fired in a high-temperature, sintering furnace to create hard, ceramic pellets of enriched uranium dioxide. The cylindrical pellets are then put into tubes of a corrosion-resistant zirconium metal alloy (Zircaloy) which are backfilled with helium to aid heat conduction and detect leakages. The finished fuel rods are grouped in fuel assemblies, called fuel bundles, that are then used to build the core of the reactor. As a safety measure PWR designs do not contain enough fissile uranium to sustain a prompt critical chain reaction (i.e, substained only by prompt neutron). Avoiding prompt criticality is important as a prompt critical chain reaction could very rapidly produce enough energy to damage or even melt the reactor (as is suspected to have occurred during the accident at the Chernobyl plant). A typical PWR has fuel assemblies of 200 to 300 rods each, and a large reactor would have about 150-250 such assemblies with 80-100 tonnes of uranium in all. Generally, the fuel bundles consist of fuel rods bundled 14x14 to 17x17. A PWR produces on the order of 900 to 1500 MWe. PWR fuel bundles are about 4 meters in length.Refuelings for most commercial PWRs is on an 18-24 month cycle. Approximately one third of the core is replaced each refueling.

Control

Generally, reactor power can be viewed as following steam (turbine) demand due to the reactivity feedback of the temperature change caused by increased or decreased steam flow. Boron and control rods are used to maintain primary system temperature at the desired point. In order to decrease power, the operator throttles shut turbine inlet valves. This would result in less steam being drawn from the steam generators. This results in the primary loop increasing in temperature. The higher temperature causes the reactor to fission less and decrease in power. The operator could then add boric acid and/or insert control rods to decrease temperature to the desired point.
Reactivity adjustments to maintain 100% power as the fuel is burned up in most commercial PWR's is normally controlled by varying the concentration of boric acid dissolved in the primary reactor coolant. The boron readily absorbs neutrons and increasing or decreasing its concentration in the reactor coolant will therefore affect the neutron activity correspondingly. An entire control system involving high pressure pumps (usually called the charging and letdown system) is required to remove water from the high pressure primary loop and re-inject the water back in with differing concentrations of boric acid. The reactor control rods, inserted through the top directly into the fuel bundles, are normally only used for power changes. In contrast, BWRs have no boron in the reactor coolant and control the reactor power by adjusting the reactor coolant flow rate.Due to design and fuel enrichment differences, naval nuclear reactors do not use boric acid.

Advantages

• PWR reactors are very stable due to their tendency to produce less power as temperatures increase, this makes the reactor easier to operate from a stability standpoint.
• PWR reactors can be operated with a core containing less fissile material than is required for them to go prompt critical. This significantly reduces the chance that the reactor will run out of control and makes PWR designs relatively safe from criticality accidents.
• Because PWR reactors use enriched uranium as fuel they can use ordinary water as a moderator rather than the much more expensive heavy water.
• PWR turbine cycle loop is separate from the primary loop, so the water in the secondary loop is not contaminated by radioactive materials.
• The reactor has high power density.
• The reactor responds to supply more power when the load increases.

Disadvantages

• The coolant water must be heavily pressurized to remain liquid at high temperatures. This requires high strength piping and a heavy pressure vessel and hence increases construction costs. The higher pressure can increase the consequences of a Loss of Coolant Accident.
• Most pressurized water reactors cannot be refueled while operating. This decreases the availability of the reactor- it has to go offline for comparably long periods of time (some weeks).
• The high temperature water coolant with boric acid dissolved in it is corrosive to carbon steel (but not stainless steel), this can result in radioactive corrosion products to circulate in the primary coolant loop. This not only limits the lifetime of the reactor, but the systems that filter out the corrosion products and adjust the boric acid concentration add significantly to the overall cost of the reactor and radiation exposure.
• Water absorbs neutrons making it necessary to enrich the uranium fuel, which increases the costs of fuel production. If heavy water is used it is possible to operate the reactor with natural uranium, but the production of heavy water requires large amounts of energy and is hence expensive.
• Because water acts as a neutron moderator it is not possible to build a fast neutron reactor with a PWR design. For this reason it is not possible to build a fast breeder reactor with water coolant.
• Because the reactor produces energy more slowly at higher temperatures, a sudden cooling of the reactor coolant could increase power production until safety systems shut down the reactor.

CANDU Reactor

CANDU Reactor

The CANDU reactor is a Pressurized Heavy Water Reactor developed initially in the late 1950s and 1960s by a partnership between Atomic Energy of Canada Limited (AECL), the Hydro-Electric Power Commission of Ontario (now known as Ontario Power Generation), Canadian General Electric (now known as GE Canada), as well as several private industry participants. The acronym "CANDU", a registered trademark of Atomic Energy of Canada Limited, stands for "CANada Deuterium Uranium". This is a reference to its deuterium-oxide (heavy water) moderator and its use of natural uranium fuel. This type of reactor is meant for those countries which do not prodce enriched uranium.Enrichment of uranium is costly and this reactor uses natural uranium as fuel and heavy water as moderator.

In heavy water reactors both the modeartor and coolant are heavy water (D2O). A great disadvantage of this type comes from this fact: heavy water is one of the most expensive liquids. However, it is worth its price: this is the best moderator. Therefore, the fuel of HWRs can be slightly (1% to 2%) enriched or even natural uranium. Heavy water is not allowed to boil, so in the primary circuit very high pressure, similar to that of PWRs, exists.

CANDU fuel is made from uranium that is naturally radioactive. Small amounts of uranium can generate large amounts of energy in the form of heat. The uranium is mined, refined and made into solid ceramic pellets (two pellets are the size of an AA battery). The pellets are put in metal tubes, which are welded together to form a fuel bundle that weighs around 23 kg.The bundle is about the size of a fireplace log and can provide enough energy for an average home for 100 years. The figure below shows the CANDU reactor and its main parts.


In CANDU reactors, the moderator and coolant are spatially separated: the moderator is in a large tank (calandria), in which there are pressure tubes surrounding the fuel assemblies. The coolant flows in these tubes only.

The advantage of this construction is that the whole tank need not be kept under high pressure, it is sufficient to pressurize the coolant flowing in the tubes. This arrangement is called pressurized tube reactor. Warming up of the moderator is much less than that of the coolant; its is simply lost for heat generation or steam production. The high temperature and high pressure coolant, similarly to PWRs, goes to the steam generator where it boils the secondary side light water. Another advantage of this type is that fuel can be replaced during operation and thus there is no need for outages.
Fission reactions in the reactor core heat a fluid, in this case heavy water (see below), which is kept under high pressure to raise its boiling point and avoid significant steam formation in the core. The hot heavy water generated in this primary cooling loop is passed into a heat exchanger heating light (ordinary) water in the less-pressurized secondary cooling loop. This water turns to steam and powers a conventional turbine with a generator attached to it. Any excess heat energy in the steam after flowing through the turbine is rejected into the environment in a variety of ways, most typically into a large body of cool water (lake, river, or ocean). More recently-built CANDU plants (such as the Darlington station near Toronto, Ontario) use a discharge-diffuser system that limits the thermal effects in the environment to within natural variations.
CANDU reactors employ two independent, fast-acting safety shutdown systems. Control rods penetrate the calandria vertically and lower into the core in the case of a safety-system trip.A second shutdown system is via gadolinium nitrate liquid "neutron poison" injection directly in to the low pressure moderator. Both systems operate via separate and independent trip logic.

CANDU-specific features and advantages

Use of natural uranium as a fuel

• CANDU is the most efficient of all reactors in using uranium: it uses about 15% less uranium than a pressurized water reactor for each megawatt of electricity produced.
• Use of natural uranium widens the source of supply and makes fuel fabrication easier. Most countries can manufacture the relatively inexpensive fuel .
• There is no need for uranium enrichment facility.
• Fuel reprocessing is not needed, so costs, facilities and waste disposal associated with reprocessing are avoided.
• CANDU reactors can be fuelled with a number of other low-fissile content fuels, including spent fuel from light water reactors. This reduces dependency on uranium in the event of future supply shortages and price increases .

Use of heavy water as a moderator

• Heavy water (deuterium oxide) is highly efficient because of its low neutron absorption and affords the highest neutron economy of all commercial reactor systems. As a result chain reaction in the reactor is possible with natural uranium fuel.
• Heavy water used in CANDU reactors is readily available. It can be produced locally, using proven technology. Heavy water lasts beyond the life of the plant and can be re-used .

CANDU reactor core design

• Reactor core comprising small diameter fuel channels rather that one large pressure vessel
• Allows on-power refueling - extremely high capability factors are possible .
• The moveable fuel bundles in the pressure tubes allow maximum burn-up of all the fuel in the reactor core.
• Extends life expectancy of the reactor because major core components like fuel channels are accessible for repairs when needed

Nuclear Power Plant Operation

Nuclear Power Plant Operation

The below diagram shows the schematic of nuclear power plant.Nuclear power generation is much similar to that of conventional steam power generation.The difference lies only in the steam generation part i.e coal or oil boiling furnance and boiler are replaced by nuclear reactor.

Thus a nuclear power plant consists of a nuclear reactor,steam generator,turbine, generator, condenser etc. as shown in the above figure.As in a conventional steam plant, water for raising steam forms a closed feed system.However, the reactor and the cooling circuit have to be heavily shielded to eliminate radiation hazards.

A nuclear power plant uses the heat generated by a nuclear fission process to drive a steam turbine which generates usable electricity.Fission is the splitting of atoms into smaller parts. Some atoms, themselves tiny, split when they are struck by even smaller particles, called neutrons. Each time this happens more neutrons come out of the split atom and strike other atoms. This process of energy release is called a chain reaction. The plant controls the chain reaction to keep it from releasing too much energy too fast. In this way, the chain reaction can go on for a long time.

Few natural elements have atoms that will split in a chain reaction. Iron, copper, silver and many other common metals will not split, or fission. There are isotopes of iron, copper, etc. that are radioactive. This means that they have an unstable nucleus and they emit radioactivity. However, just being radioactive does not mean that they will fission, or split. But uranium will. So uranium is suitable to fuel a nuclear power plant.

As atoms split and collide, they heat up. The plant uses this heat to create steam.The heat is transfered to the water through heat exchanging tubes in steam generator in the primary loop.After extractig this heat, water is converted in to steam and collected at the top of steam generator.The pressure of the expanding steam turns a turbine which is connected to a generator in the secondary loop.After rotating turbine - generator set steam passes to the condenser.After that the function of condenser and coling towers is same as that of thermal plant.

After the steam is made, a nuclear plant operates much like a fossil fuel fired plant: the turbine spins a generator. The whirling magnetic field of the generator produces electricity. The electricity then goes through wires strung on tall towers you might see along a highway to an electrical substation in your neighborhood where the power is regulated to the proper strength. Then it goes to your home.

In the case of nuclear power plant operation the following factors must be considered

• Control -- Keeping the nuclear reaction from dying out or exploding.
• Safety -- If something goes wrong it can be contained.
• Refueling -- Adding more nuclear fuel without stoping the reactor.
• Waste production -- The byproducts of the reaction must be manageable.
• Efficiency -- Capture as much of the heat as possible.

Control is the most important aspect to a design. When an atom of nuclear fuel (uranium) absorbs a neutron, the uranium will fission into two smaller atoms (waste) and release one to three neutrons. The kinetic energy of the waste is used to heat the water for the steam turbine. The neutrons are used to fission the next lot of uranium atoms and the process continues. If none of these neutrons are absorbed by another uranium atom then the reaction dies out. If too many neutrons are absorbed then the reaction grows extremely quickly and could explode. Current reactor designs are most usefully classified by how they ensure this nuclear reaction is kept at a level which produces power without getting out of hand.
The Nuclear Regulatory Commission (NRC), part of our government, makes sure nuclear power plants in the United States protect public health and safety and the environment. The NRC licenses the use of nuclear material and inspects users to make sure they follow the rules for safety.
Since radioactive materials are potentially harmful, nuclear power plants have many safety systems to protect workers, the public, and the environment. These safety systems include shutting the reactor down quickly and stopping the fission process, systems to cool the reactor down and carry heat away from it and barriers to contain any radioactivity and prevent it from escaping into the environment.
One of the greatest benefits of nuclear plants is that they have no smoke stacks! The big towers many people associate with nuclear plants are actually for cooling water used to make steam. (Some other kinds of plants have these towers, too.) The towers spread the water out so as much air as possible can reach it and cool it down. Most water is then recycled into the plant.

Nuclear power plants are very clean and efficient to operate. However, nuclear power plants have some major environmental risks. Nuclear power plants produce radioactive gases. These gases are to be contained in the operation of the plant. If these gases are released into the air, major health risks can occur. Nuclear plants use uranium as a fuel to produce power. The mining and handling of uranium is very risky and radiation leaks can occur. The third concern of nuclear power is the permanent storage of spent radioactive fuel. This fuel is toxic for centuries, handling and disposal is an ongoing environmental issue.

Transmission Line,Representation,Types and Applications

Transmission Line

A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission. Components of transmission lines include wires, coaxial cables, dielectric slabs, optical fibers, electric power lines, and waveguides.

An electric transmission line can be generally represented by a series combination of resistance,inductance and shunt combination of conductance and capacitace as shown below.The transmission line model represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line:

Transmission lines are basically circuits with distributed constants i.e R,L,C and G are distributed along the whole length of line.each small length at any section of the line will have its own values and concentration of all such parameters for complete length of line in to a single one is not possible.In the above figure

• The distributed resistance R of the conductors is represented by a series resistor (expressed in ohms per unit length).
• The distributed inductance L (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (henries per unit length).
• The capacitance C between the two conductors is represented by a shunt capacitor C (farads per unit length).
• The conductance G of the dielectric material separating the two conductors is represented by a conductance G shunted between the signal wire and the return wire (siemens per unit length).

Among the parameters R,L,G and C , R and G are least important in the sense that they do not affect much the total equivalent impedance of the line and hence the transmission capacity.They are very much important when transmission efficiency and economy are to be evaluated as they completely determine the real transmission line losses.

Practical types of electrical transmission line

Coaxial cable
Coaxial lines confine the electromagnetic wave to the area inside the cable, between the center conductor and the shield. The transmission of energy in the line occurs totally through the dielectric inside the cable between the conductors. Coaxial lines can therefore be bent and twisted (subject to limits) without negative effects, and they can be strapped to conductive supports without inducing unwanted currents in them.
In radio-frequency applications up to a few gigahertz, the wave propagates in the transverse electric and magnetic mode (TEM), which means that the electric and magnetic fields are both perpendicular to the direction of propagation. However, above a certain frequency called the cutoff frequency, the cable behaves as a waveguide, and propagation switches to either a transverse electric (TE) or a transverse magnetic (TM) mode or a mixture of modes. This effect enables coaxial cables to be used at microwave frequencies, although they are not as efficient as the more expensive, purpose-built waveguides.
The most common use for coaxial cables is for television and other signals with bandwidth of multiple Megahertz. In the middle 20th Century they carried long distance telephone connections.

Microstrip
A microstrip circuit uses a thin flat conductor which is parallel to a ground plane. Microstrip can be made by having a strip of copper on one side of a printed circuit board (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the dielectric constant of the insulating layer determine the characteristic impedance.

Stripline
A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line.

Balanced lines
Lecher linesLecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are used at frequencies between HF/VHF where lumped components are used, and UHF/SHF where resonant cavities are more practical.

General applications of transmission lines

Transferring signals from one point to another
 Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss. One familiar example is the down lead from a TV or radio aerial to the receiver.

Pulse generation

Transmission lines are also used as pulse generators. By charging the transmission line and then discharging it into a resistive load, a rectangular pulse equal in length to twice the electrical length of the line can be obtained, although with half the voltage. A Blumlein transmission line is a related pulse forming device that overcomes this limitation. These are sometimes used as the pulsed energy sources for radar transmitters and other devices.

Stub filters
If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it will function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it is 'working backwards'. One method recommended in the RSGB's radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the feeder delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics.

Performance of Transmission Lines

Performance of Transmission Lines

 

The performance of a power system is mainly dependent on the performance of the transmission lines in the system.It is necessary to calculate the voltage,current and power at any point on a transmission line provided the values at one point are known.

The transmission line performance is governed by its four parameters - series resistance and inductance,shunt capacitance and conductance.All these parameters are distributed over the length of the line.The insulation of a line is seldom perfect and leakage currents flow over the surface of insulators especially during bad weather.This leakage is simulated by shunt conductance.The shunt conductance is in parallel with the system capacitance.Generally the leakage currents are small and the shunt conductance is ignored in calculations.

Performance of transmission lines is meant the determination of efficiency and regulation of lines.The efficiency of transmission lines is defined as

The end of the line where load is connected is called the receiving end and where source of supply is connected is called the sending end.

The Regulation of a line is defined as the change in the receiving end voltage, expressed in percent of full load voltage, from no load to full load, keeping the sending end voltage and frequency constant.

 

 

 

 

 

Classification of Transmission Lines

Classification of transmission lines

Transmission lines are classified as short, medium and long. When the length of the line is less than about 80Km the effect of shunt capacitance and conductance is neglected and the line is designated as a short transmission line. For these lines the operating voltage is less than 20KV.

For medium transmission lines the length of the line is in between 80km - 240km and the operating line voltage wil be in between 21KV-100KV.In this case the shunt capacitance can be assumed to be lumped at the middle of the line or half of the shunt capacitance may be considered to be lumped each end of the line.The two representations of medium length lines are termed as nominal-T and nominal- π respectively.

Lines more than 240Km long and line voltage above 100KV require calculations in terms of distributed parameters.Such lines are known as long transmission lines.This classification on the basis of length is more or less arbitrary and the real criterion is the degree of accuracy required.

Short Transmission Line : Equivalent Circuit and Phasor Diagram

Short Transmission Line

The equivalent circuit and vector diagram of a short transmission line are shown in the figure given below.In the equivalent circuit short transmission line is represented by the lumped parameters R and L. R is the resistance (per phase) L is the inductance (per phase) of the entire transmission line.As said earlier the effect of shunt capacitance and conductance is not considered in the equivalent circuit.The line is shown to have two ends : sending end (designated by the subscript S) at the generator, and the receiving end (designated R) at the load.

The phasor diagram is drawn taking Ir, the receiving end current as the reference.


The terms with in the simple brackets is small as compared to unity, using binomial expansion and limiting only to second term
Vs ≈ Vr + IrR cosΦr + IrX sinΦr
Here Vs is the sending end voltage corresponding to a particular load current and power factor condition. It can be seen from the equivalent circuit that the receiving end voltage under no load is same as the sending end voltage under full load condition i.e Vr(no load) = Vs . Therefore
where Vr and Vx are the per unit values of resistance and reactance of the line.From the equivalent circuit diagram we can observe that
Vs = Vr + Ir ( R + jX) = Vr + IrZ
Is = Ir
In a four terminal passive network the voltage and current on the receiving end and sending end are related by following pair of equations
Vs = AVr + BIr
Is = CVr + DIr
Comparing the above two sets of equations, for a short transmission line A = 1, B = Z, C = 0, D = 1. ABCD constants can be used for calculation of regulation of the line as follows:
Normally the quantities P,Ir and cosΦr at the receiving end are given and ofcourse the ABCD constants.Then determine sending end voltage using the relation Vs = AVr + BIr. Vr(no load) at the receivind end is given by Vs/A when Ir = 0.