Single Three Phase Transformer vs bank of three Single Phase Transformers

It is found that generation, transmission and distribution of electrical power are more economical in three phase system than single phase system. For three phase system three single phase transformers are required. Three phase transformation can be done in two ways, by using single three phase transformer or by using a bank of three single phase transformers. Both are having some advantages over other. Single 3 phase transformer costs around 15% less than bank of three single phase transformers. Again former occupies less space than later. For very big transformer, it is impossible to transport large three phase transformer to the site and it is easier to transport three single phase transformers which is erected separately to form a three phase unit. Another advantage of using bank ofthree single phase transformers is that, if one unit of the bank becomes out of order, then the bank can be run as open delta.

Connection of Three Phase Transformer

A Variety of connection of three phase transformer are possible on each side of both a single 3 phase transformer or a bank of three single phase transformers.

Transformer Insulating Oil and Types of Transformer Oil

Insulating oil in an electrical power transformer is commonly known as Transformer Oil. It is normally obtained by fractional distillation and subsequent treatment of crude petroleum. That is why this oil is also known as Mineral Insulating Oil. Transformer Oil serves mainly two purposes one it is liquid insulation in electrical power transformer and two it dissipates heat of the transformer i.e. acts as coolant. In addition to these, this oil serves other two purposes, it helps to preserve the core and winding as these are fully immersed inside oil and another important purpose of this oil is, it prevents direct contact of atmospheric oxygen with cellulose made paper insulation of windings, which is susceptible to oxidation.

Types of Transformer Oil

Generally there are two types of Transformer Oil used in transformer,

1. Paraffin based Transformer Oil

2. Naphtha based Transformer Oil

Core of Transformer and Design of Transformer Core

In a electrical power transformer there are primary, secondary and may be tertiary windings. The performance of a transformer mainly depends upon the flux linkages between these windings. For efficient flux linking between these winding one low reluctance magnetic path common to all windings, should be provided in the transformer. This low reluctance magnetic path in transformer is known as core of transformer.

Influence of Diameter of Transformer Core

Let us consider, the diameter of transformer core be ′D′

Transformer Cooling System and Methods

The main source of heat generation in transformer is its copper loss or I2R loss. Although there are other factors contribute heat in transformer such as hysteresis & eddy current losses but contribution of I2R loss dominate them. If this heat is not dissipated properly, the temperature of the transformer will rise continually which may cause damages in paper insulation and liquid insulation medium of transformer. So it is essential to control the temperature within permissible limit to ensure the long life of transformer by reducing thermal degradation of its insulation system. In Electrical Power transformer we use external transformer cooling system to accelerate the dissipation rate of heat of transformer.There are different transformer cooling methods available for transformer, we will now explain one.

Parallel operation of Transformers

It is economical to installed numbers of smaller rated transformers in parallel than installing a bigger rated electrical power transformer. This has mainly the following advantages,

1) To maximize electrical power system efficiency: Generally electrical power transformer gives the maximum efficiency at full load. If we run numbers oftransformers in parallel, we can switch on only those transformers which will give the total demand by running nearer to its full load rating for that time. When load increases we can switch no one by one other transformer connected in parallel to fulfill the total demand. In this way we can run the system with maximum efficiency.

2) To maximize electrical power system availability: If numbers of transformers run in parallel we can take shutdown any one of them for maintenance purpose. Other parallel transformers in system will serve the load without total interruption of power.

3) To maximize power system reliability: if nay one of the transformers run in parallel, is tripped due to fault other parallel transformers is the system will share the load hence power supply may not be interrupted if the shared loads do not make other transformers over loaded.

4) To maximize electrical power system flexibility: Always there is a chance of increasing or decreasing future demand of power system. If it is predicted that power demand will be increased in future, there must be a provision of connecting transformers in system in parallel to fulfill the extra demand because it is not economical from business point of view to install a bigger rated single transformer by forecasting the increased future demand as it is unnecessary investment of money. Again if future demand is decreased, transformers running in parallel can be removed from system to balance the capital investment and its return.

Tertiary Winding of Transformer | Three Winding Transformer

In some high rating transformer, one winding, in addition to its primary and secondary winding, is used. This additional winding, apart from primary and secondary windings, is known as Tertiary Winding of Transformer. Because of this third winding, the transformer is called Three Winding Transformeror 3 Winding Transformer.

Advantages of using tertiary winding in transformer


Tertiary Winding is provided in Electrical Power Transformer to meet one or more of the following requirements

1. It reduces the unbalancing in the primary due to unbalancing in three phase load

2. It redistributed the flow of fault current

3. Sometime it is required to supply an auxiliary load in different voltage level in addition to its main secondary load. This secondary load can be taken from tertiary winding of three winding transformer.

4. As the tertiary winding is connected in delta formation in 3 winding transformer, it assists in limitation of fault current in the event of a short circuit from line to neutral.

Auto Transformer

Auto transformer is kind of electrical transformer where primary and secondary shares same common single winding.

Theory of Auto Transformer

In Auto Transformer, one single winding is used as primary winding as well as secondary winding. But in two windings transformer two different windings are used for primary and secondary purpose. A diagram of auto transformer is shown below,

The winding AB of total turns N1 is considered as primary winding. This winding is tapped from point ′C′ and the portion BC is considered as secondary. Let's assume the number of turns in between points ′B′ and ′C′ is N2.

Losses in Transformer

As the electrical transformer is a static device, mechanical loss in transformer normally does not come into picture. We generally consider only electrical losses in transformer. Loss in any machine is broadly defined as difference between input power and output power.

When input power is supplied to the primary of transformer, some portion of that power is used to compensate core losses in transformer i.e.Hysteresis loss in transformer and Eddy Current loss in transformer core and some portion of the input power is lost as I2R loss and dissipated as heat in the primary and secondary winding, as because these windings have some internal resistance in them. The first one is called core loss or iron loss in transformer and later is known as ohmic loss or copper loss in transformer. Another loss occurs in transformer, known as Stray Loss, due to Stray fluxes link with the mechanical structure and winding conductors.

Voltage Regulation of Transformer

Definition

The voltage regulation is the percentage of voltage difference between no load and full load voltages of a transformer with respect to its full load voltage.
Explanation of Voltage Regulation of Transformer

Say a electrical power transformer is open circuited means load is not connected with secondary terminals. In this situation the secondary terminal voltage of the transformer will be its secondary induced emf E2. Whenever full load is connected to the secondary terminals of the transformer, rated current I2 flows through the secondary circuit and voltage drops comes into picture. At this situation, primary winding will also draw equivalent full load current from source. The voltage drop in the secondary is I2Z2 where Z2 is the secondary impedance of transformer. If now, at this loading condition any one measures the voltage between secondary terminals, he or she will get voltage V2 across load terminals which is obviously less than no load secondary voltage E2 and this is because of I2Z2 voltage drop in the transformer.

Equivalent Circuit of Transformer referred to Primary and Secondary

Equivalent Circuit of Transformer

Equivalent impedance of Transformer is essential to be calculated as because the electrical power transformer is an electrical power systemequipment so for estimating different parameters of electrical power system it may be required to calculate total internal impedance of anelectrical power transformer viewing from primary side or secondary side as per requirement. This calculation requires equivalent circuit of transformer referred to primary or equivalent circuit of transformer referred to secondary sides respectively. Percentage impedance is also very essential parameter of transformer. Special attention is to be given to this parameter during installing a transformer in an existing electrical power system. Percentage impedance of different power transformers should be properly matched during parallel operation of these transformers. The percentage impedance can be derived from equivalent impedance of transformer so it can be said that equivalent circuit of transformer is also required during calculation of % impedance.

Resistance & Leakage Reactance or Impedance of Transformer

Leakage Reactance of Transformer

All the flux in transformer will not be able to link with both the primary and secondary windings. A small portion of flux will link either winding but not both. This portion of flux is called leakage flux. Due to this leakage flux in transformer there will be a self - reactance in the concerned winding. This self-reactance of transformer is alternatively known as leakage reactance of transformer. This self - reactance associated with resistance of transformer is impedance. Due to this impedance of transformer there will be voltage drops in both primary and secondary transformer windings.

EMF Equation of Transformer | Turns Voltage Transformation Ratio of Transformer

EMF Equation of transformer can be established in very easy way. Actually in electrical power transformer, one alternating electrical source is applied to the primary winding and due to this, magnetizing current flows through the primary which produces alternating flux in the core of transformer. This flux links with both primary and secondary windings. As this flux is alternating in nature there must be a rate of change of flux. According toFaraday's law of electromagnetic induction if any coil or conductor links with any changing flux, there must be an induced emf in it. As the electric current source to primary, is sinusoidal, the flux induced by it will be also sinusoidal. Hence the function of flux may be considered as a sine function. Mathematically derivative of that function will give a function for rate of change of flux linkage with respect to time. This later function will be a cosine function since d(sinθ)/dt = cosθ. So if we derive the expression for rms value of this cosine wave and multiply it with number of turns of the winding we will easily get the expression for rms value of induced emf of that winding. In this way we can easily derive the emf equation of transformer.

Let, T is number of turns in a winding,

Theory of Transformer on load and no load operation

We have discussed about theory of Ideal Transformer for better understanding of actual elementary theory of transformer. Now we will go through one by one practical aspects of an electrical power transformer and try to draw vector diagram of transformer in every step. As we said that inideal transformer there are no core losses in transformer i.e. loss free core of transformer. But in practical transformer there are hysteresis and eddy current losses in transformer core.

Ideal Transformer

Definition of Ideal Transformer

An Ideal Transformer is an imaginary transformer which does not have any loss in it, means no core losses, copper losses and any other losses in transformer. Efficiency of this transformer is considered as 100%.

Working Principle of transformer

The working principle of transformer is very simple. It depends uponFaraday's law of electromagnetic induction. Actually mutual induction between two or more winding is responsible for transformation action in an electrical transformer.
Faraday's laws of Electromagnetic Induction

According to these Faraday's law,

"Rate of change of flux linkage with respect to time is directly proportional to the induced EMF in a conductor or coil".

Electrical Power Transformer | Definition and Types of Transformer

A transformer is a static machine used for transforming power from one circuit to another without changing frequency. This is very basic definition of transformer.

History of Transformer

The History of transformer commenced in the year of 1880. In the year of 1950, 400KV electrical power transformer was first introduced in high voltage electrical power system. In the early 1970s unit rating as large as 1100MVA were produced and 800KV and even higher KV class transformers were manufactured in year of 1980.

Use of Power Transformer

Generation of Electrical Power in low voltage level is very much cost effective. Hence Electrical Power are generated in low voltage level. Theoretically, this low voltage leveled power can be transmitted to the receiving end. But if the voltage level of a power is increased, the electric current of the power is reduced which causes reduction in ohmic or I2R losses in the system, reduction in cross sectional area of the conductor i.e. reduction in capital cost of the system and it also improves the voltage regulation of the system. Because of these, low leveled power must be stepped up for efficient electrical power transmission. This is done by step up transformer at the sending side of the power system network. As this high voltage power may not be distributed to the consumers directly, this must be stepped down to the desired level at the receiving end with help of step down transformer. These are the use of electrical power transformerin the Electrical Power System.

Two winding transformers are generally used where ratio between High Voltage and Low Voltage is greater than 2. It is cost effective to use Auto transformerwhere the ratio between High Voltage and Low Voltage is less than 2. Again Three Phase Single Unit Transformer is more cost effective than a bank of three Single Phase Transformer unit in a three phase system. But still it is preferable to use later where power dealing is very large since such large size of Three Phase Single Unit Power Transformer may not be easily transported from manufacturer's place to work site.

Frog Leg Winding | Drum Winding | Gramme Ring Winding

Frog Leg Winding

Frog leg winding is a combination of a multiplex wave and a simplex lap winding in the same slots. It retains the advantages of both lap and wave windings without their inherit disadvantages.
Both lap and wave windings have equal number of parallel paths and they are conncted to the same commutator.The frog-leg winding have as many parallel paths as duplex lap winding because the simplex lap winding portion supplies P no. of parallel paths and the multiplex-wave section also provides Pno. of parallel paths, then total being 2P no. of paths in parallel.

Methods of Improving Commutation

To make the commutation satisfactory we have to make sure that the current flowing through the coil completely reversed during the commutation period attains its full value.

There are two main methods of improving commutation. These are
1) Resistance Commutation
2) E.m.f. Commutation

Commutation in DC Machine

The voltage generated in the armature, placed in a rotating magnetic field, of a dc generator is alternating in nature. The commutation in DC machine or more specifically commutation in DC generator is the process in which generated alternating current in the armature winding of a dc machine is converted into direct current after going through the commutator and the stationary brushes.

Applications of DC Generators

There are various types of dc generators available for several types of services. The applications of these dc generators based on their characteristic are discussed below:

DC Generators Performance Curves

Performance curves of a dc generator is that curves which shows the ability of delivering output voltage of a dc generator with the change in load current from no load to full load. These are also called characteristic curves. From the performance curve we can get a clear idea about the voltage regulation of various kind of dc generators. The lower the voltage regulation will be, the performance of the generator will be better.

Characteristic of DC Compound Wound Generators

In compound wound generators both the field windings are combined (series and shunt). This type of generators can be used as either long shunt or short shunt compound wound generators as shown in the diagram below. In both the cases the external characteristic of the generator will be nearly same.The compound wound generators may be cumulatively compounded or differentially compounded (discussed earlier in the type of generators).

Characteristics of Series Wound DC Generator

In these types of generators the field windings, armature windings and external load circuit all are connected in series as shown in figure below.

Therefore, the same current flows through armature winding, field winding and the load.

Let, I = Ia = Isc = IL
Here, Ia = armature current
Isc = series field current
IL = load current

There are generally three most important characteristics of series wound dc generator which show the relation between various quantities such as series field current or excitation current, generated voltage, terminal voltage and load current.

Characteristic of Shunt Wound DC Generator

In shunt wound dc generators the field windings are connected in parallel with armature conductors as shown in figure below. In these type of generators the armature current Ia divides in two parts. One part is the shunt field current Ish flows through shunt field winding and the other part is the load current IL goes through the external load.


Three most important characteristic of shunt wound dc generators are discussed below:

Magnetization Curve of DC Generator

Magnetization curve of a dc generator is that curve which gives the relation between field current and the armature terminal voltage on open circuit.

Hopkinson’s Test

Hopkinson's test is another useful method of testing the efficiency of a dc machine. It is a full load test and it requires two identical machines which are coupled to each other. One of these two machines is operated as a generator to supply the mechanical power to the motor and the other is operated as a motor to drive the generator. For this process of back to back driving the motor and the generator, Hopkinson's test is also called back-to-back test or regenerative test.

If there are no losses in the machine, then no external power supply would have needed. But due to the drop in the generator output voltage we need an extra voltage source to supply the proper input voltage to the motor. Hence, the power drawn from the external supply is therefore used to overcome the internal losses of the motor-generator set.

Swinburne’s Test of DC Machine

This method is an indirect method of testing a dc machine. It is named after Sir James Swinburne. Swinburne's test is the most commonly used and simplest method of testing of shunt and compound wound dc machines which have constant flux. In this test the efficiency of the machine at any load is pre-determined. We can run the machine as a motor or as a generator. In this method of testing no load losses are measured separately and eventually we can determine the efficiency.

The circuit connection for Swinburne's test is shown in figure below. The speed of the machine is adjusted to the rated speed with the help of the shunt regulator R as shown in figure.

Connection Diagram of Swinburne's Test

Differential Protection

1. Differential  Protection

"A differential relay responds to vector difference between two or more similar electrical quantities "

From the definition the following aspects are known ; -

1- The differential relay has at least two actuating quantities say I₁, I₂

2- The two or more quantities should be similar i.e. current/current.

3- The relay responds to the vector difference between the tow i.e. to I₁-I₂,  which includes magnitude and/or phase angle difference.

       Differential protection is generally unit protection. The protected zone is exactly determined by location of CT's and VT's. The vector difference is achieved by suitable connections of current transformer or voltage transformer secondaries.

Methods of arranging Conductors

There are various methods of arranging the conductors over the line supports.

i) Single phase circuits :

       There are two types of arrangements in single phase circuits viz single circuit and double circuit which are respectively shown in the Fig. 1(a) and (b). In double circuit there are again two subtypes of arrangements viz horizontal and vertical disposition.

Fig. 1

INDUCTIVE INTERFERENCE WITH NEIGHBOURING CIRCUIT

 In practice it is observed that the power lines and the communication lines run along the same path. Sometimes it can also be seen that both these lines run on same supports along the same route. The transmission lines transmit bulk power with relatively high voltage. Electromagnetic and electrostatic fields are produced by these lines having sufficient magnitude. Because of these fields, voltages and currents are induced in the neighbouring communication lines. Thus it gives rise to interference of power line with communication circuit.

       Due to electromagnetic effect, currents are induced which is superimposed on speech current of the neighbouring communication line which results into distortion. The potential of the communication circuit as a whole is raised because of electrostatic effect and the communication apparatus and the equipments may get damaged due to extraneous voltages. In the worst situation, the faithful transmission of message becomes impossible due to effect of these fields. Also the potential of the apparatus is raised above the ground to such an extent that the handling of telephone receiver becomes extremely dangerous.

       The electromagnetic and the electrostatic effects mainly depend on what is the distance between power and communication circuits and the length of the route over which they are parallel. Thus it can be noted that if the distortion effect and potential rise effect are within permissible limits then the communication will be proper. The unacceptable disturbance which is produced in the telephone communication because of power lines is called Telephone Interference.

       There are various factors influencing the telephone interference. These factors are as follows

1) Because of harmonics in power circuit, their frequency range and magnitudes.

2) Electromagnetic coupling between power and telephone conductor.

       The electric coupling is in the form of capacitive coupling between power and telephone conductor whereas the magnetic coupling is through space and is generally expressed in terms of mutual inductance at harmonic frequencies.

3) Due to unbalance in power circuits and in telephone circuits.

4) Type of return telephone circuit i.e. either metallic or ground return.

5) Screening effects.

Capacitance of 3-Phase Double Circuit with Unsymmetrical Spacing but Transposed

 Consider the arrangement of conductors shown in the Fig. 1. It consists of three phase double circuit. The radius of each conductor r.

Fig. 1

      

Capacitance of 3-Phase Line with more than One Circuit

Consider the arrangement of conductors shown in the Fig. 1.

Fig. 1

      

BUNDLED CONDUCTORS

The Fig. 1 shows the arrangement if the conductors are bundled one

Fig. 1

       The conductors of any one bundle are in parallel and charge per bundle is assumed to divide equally between the conductors of bundle.

       The composite or stranded conductors touch each other while the bundled conductors are away from each other. The typical distance is about 30 cm and more. The conductors of each phase are connected by using connecting wires at particular length.

       Due excessive corona loss, the round conductors are not feasible for use for voltage level more than 230 kV. It is preferable to use hollow conductor in substations while bundled conductors in transmission lines.

       Following are advantages of bundled conductors.

1. Low radio interference and corona loss.

2. Reduced voltage gradient at conductor surface.

3. Increase in capacitance.

4. Low reactance due to increase in self GMD.

5. Increase in surge impedance loading.

       If the charge on phase a is q_a then charge on each of the conductors a and 'a' will be q_a/2. Same is the case with remaining two phases.

       This equation is similar to the expression we have written for 3 phase line with unsymmetrical spacing. Combining the terms we get

       Thus, for a two strand bundle

       For a three strand bundle

1.1 Stranded Conductor

       The stranded conductor usually has a central wire which is surrounded by the layers of wires. These layers consists of 6, 12, 18, ......... wires successively. Thus the total strands are 7, 13, 19  .............. .

       Such a stranded conductor with 37 strands is shown in the Fig. 2.

Fig. 2

       Let             d = diameter of each strand

       Then the total diameter of a stranded conductor (cable) is given by,

                         d_c = (2 n + 1) d

       where n = number of layers in which the strands are arranged around central strand.

       The stranded conductor is specified as number of strands and diameter of strand. 

       For example 7/0.295 mm which indicates 7 strands with 0.295 mm diameter of each strand.

       If at all the number of layers are not specified then the number of layers can be calculated as number of strands and layers are related to each other by the equation,

                             x = 3n² + 3n + 1

       where            x = number of strands

       and                n = number of layers

       The stranded number of strands in each successive layer from inner to outer is 6, 12, 18, 24 .......

Effect of Earth on Capacitance of Transmission Line

The capacitance of transmission line is affected by the presence of earth. Because of earth, electric field of a line is reduced. If we assume that the earth is a perfect conductor in the form of a horizontal plane of infinite extent, we realize that the electric field of charged conductors above the earth is not the same as it would be if the equipotential surface of earth were not present.

      

Capacitance of a 3-Phase Line With Unsymmetrical Spacing

The calculation of capacitance in case of conductors in three phase system which are not equally spaced is difficult. If the line is untransposed the capacitances of each phase to neutral is not same.

       In case of transposed line the average capacitance of each line to neutral over a complete transposition cycle is same as the average capacitance to neutral of any other phase. Each conductor occupies the same position of every other conductor after equal distance. The effect of unsymmetry between the lines is small and calculations are carried out by considering transposition of lines.

      

Capacitance of a 3ph Line With Equilateral Spacing

Consider the three conductors a, b and c of 3 phase overhead transmission line having the charges q_a , q_b and q_c  respectively as shown in Fig. 1. Let the conductors be separated from each other by a distance of d from each other and placed on the vertices of equilateral triangle.

F ig. 1

       The radius of each conductor is say r. The voltage V_ab of the three phase line due to only charges on conductors a and b is given by,

       Voltage V_ab due to only charge q_c  is zero as uniform charge distribution over the surface of the conductor is equivalent to a concentrated charge at the centre of conductor.

       Considering all the three charges in writing the voltage equation we have,

       Adding equations (1) and (2),

       The voltages are sinusoidal and expressed as the phasors. In absence of other charges in the vicinity the sum of the charges is zero i.e. 

               q_a  + q_b  +  q_c  = 0

.^..            q_b  +  qc  = - q_a  

        The Fig. 2 shows phasor diagram of balanced voltages of three phase line.

Fig. 2

       Adding above equations we get,

       For air, ε_r = 1

       It can be seen that capacitance to neutral for single phase and equilaterally spaced three phase lines is same.

       The current associated with capacitance of a transmission line is termed as charging current. In case of single phase circuits, the charging current of line to line voltage and line to line susceptance.

                               I_C = j  ω C_ab V_ab

       In case of three phase circuits, the charging current is found by product of voltage to neutral and capacitive susceptance to neutral. The charging current obtained is for one phase. The current in any phase is given by,

                               I_C = j  ω C_n V_an

The charging current is not same everywhere as the rms voltage along line varies. For obtaining the charging current the value of voltage used is that for which the line is designed which may not be actual voltage at either generating station or a load.

Capacitance of Single Phase Line

Capacitance between the two conductors of a two wire line is the charge on the conductor per unit of potential difference between them. Capacitance of the line per unit length is given by,

                                      C = q/v   F/m

       The capacitance of single phase line is obtained by substituting in above equation v in terms of q.

      

Potential Difference between Two Points due to a Charge

The potential difference between any two points is nothing but the work done in joules per coulomb required to move a coulomb of charge between the two points. The force on a charge in the field is measured by electric field intensity which is equal to the force in newtons per coulomb on a coulomb charge at the point considered and is measured in volts per meter.

       Consider a long straight wire carrying positive charge of q c/m as shown in the Fig. 1.

Fig. 1

       Consider two points P₁ and P₂ located at a distance of  D₁ and D₂ from centre of wire. There is positive charge on wire which will repel when a positive charge is placed in the field. If we want to move charge from point P₂ to P₁ then work must be done on positive charge. Here P₁ is at higher potential than P₂. If the charge moves from P₁ to P₂, it expends energy which is nothing but voltage drop from P₁ to P₂. The path followed does not affect the potential difference.

       In order to find the voltage drop from P₁ to P₂ is to obtain the voltage between equipotential surfaces passing through P₁ and P₂.

       The voltage drop between P₁ and P₂ is,

       The voltage drop between two points may be either positive or negative depending upon the charge causing the potential difference is positive or negative. It also depends upon whether the voltage drop is computed from a point near the conductor to a point far away or vice versa.