Electrical machines-II

UNIT-I

Electrical Transformer - Basic construction, working and types

Electrical transformer is a static electrical machine which transforms electrical power from one circuit to another circuit, without changing the frequency. Transformer can increase or decrease the voltage with corresponding decrease or increase in current.

Working principle of transformer

 The basic principle behind working of a transformer is the phenomenon of mutual induction between two windings linked by common magnetic flux. The figure at right shows the simplest form of a transformer. Basically a transformer consists of two inductive coils; primary winding and secondary winding. The coils are electrically separated but magnetically linked to each other. When, primary winding is connected to a source of alternating voltage, alternating magnetic flux is produced around the winding. The core provides magnetic path for the flux, to get linked with the secondary winding. Most of the flux gets linked with the secondary winding which is called as 'useful flux' or main 'flux', and the flux which does not get linked with secondary winding is called as 'leakage flux'.  As the flux produced is alternating (the direction of it is continuously changing), EMF gets induced in the secondary winding according to Faraday's law of electromagnetic induction. This emf is called 'mutually induced emf', and the frequency of mutually induced emf is same as that of supplied emf. If the secondary winding is closed circuit, then mutually induced current flows through it, and hence the electrical energy is transferred from one circuit (primary) to another circuit (secondary).

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Basic construction of transformer

Basically a transformer consists of two inductive windings and a laminated steel core. The coils are insulated from each other as well as from the steel core. A transformer may also consist of a container for winding and core assembly (called as tank), suitable bushings to take our the terminals, oil conservator to provide oil in the transformer tank for cooling purposes etc. The figure at left illustrates the basic construction of a transformer.

In all types of transformers, core is constructed by assembling (stacking) laminated sheets of steel, with minimum air-gap between them (to achieve continuous magnetic path). The steel used is having high silicon content and sometimes heat treated, to provide high permeability and low hysteresis loss. Laminated sheets of steel are used to reduce eddy current loss. The sheets are cut in the shape as E,I and L. To avoid high reluctance at joints, laminations are stacked by

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alternating the sides of joint. That is, if joints of first sheet assembly are at front face, the joints of following assemble are kept at back face.

Types of transformers

Transformers can be classified on different basis, like types of construction, types of cooling etc.

(A) On the basis of construction, transformers can be classified into two types as; (i) Core type transformer and (ii) Shell type transformer, which are described below.

(i) Core type transformer

In core type transformer, windings are cylindrical former wound, mounted on  the core limbs as shown in the figure above. The cylindrical coils have different layers and each layer is insulated from each other. Materials like paper, cloth or mica can be used for insulation. Low voltage windings are placed nearer to the core, as they are easier to insulate.

(ii) Shell type transformer

The coils are former wound and mounted in layers stacked with insulation between them. A shell type transformer may have simple rectangular form (as shown in above fig), or  it may have a distributed form.

(B) On the basis of their purpose

1. Step up transformer: Voltage increases (with subsequent decrease in current) at secondary.

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2. Step down transformer: Voltage decreases (with subsequent increase in current) at secondary.

(C) On the basis of type of supply

1. Single phase transformer2. Three phase transformer

(D) On the basis of their use

1. Power transformer: Used in transmission network, high rating2. Distribution transformer: Used in distribution network, comparatively lower rating than

that of power transformers.3. Instrument transformer: Used in relay and protection purpose in different instruments in

industrieso  Current transformer (CT)o Potential transformer (PT)

(E) On the basis of cooling employed

1. Oil-filled self cooled type2. Oil-filled water cooled type3. Air blast type (air cooled)

Ideal transformer and it's characteristics

An ideal transformer is an imaginary transformer which has- no copper losses (no winding resistance)- no iron loss in core- no leakage fluxIn other words, an ideal transformer gives output power exactly equal to the input power. The efficiency of an idea transformer is 100%. Actually, it is impossible to have such a transformer in practice, but ideal transformer model makes problems easier.

Characteristics of ideal transformer

Zero winding resistance: It is assumed that, resistance of primary as well as secondary winding of an ideal transformer is zero. That is, both the coils are purely inductive in nature.

Infinite permeability of the core: Higher the permeability, lesser the mmf required for flux establishment. That means, if permeability is high, less magnetizing current is required to magnetize the transformer core.

No leakage flux: Leakage flux is a part of magnetic flux which does not get linked with secondary winding. In an ideal transformer, it is assumed that entire amount of flux get linked with secondary winding (that is, no leakage flux).

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100% efficiency: An ideal transformer does not have any losses like hysteresis loss, eddy current loss etc. So, the output power of an ideal transformer is exactly equal to the input power. Hence, 100% efficiency.

Now, if an alternating voltage V1 is applied to the primary winding of an ideal transformer, counter emf E1 will be induced in the primary winding. As windings are purely inductive, this induced emf E1 will be exactly equal to the apply voltage but in 180 degree phase opposition. Current drawn from the source produces required magnetic flux. Due to primary winding being purely inductive, this current lags 90° behind induced emf E1. This current is called magnetizing current of the transformer Iμ. This magnetizing current Iμ produces alternating magnetic flux Φ. This flux Φ gets linked with the secondary winding and emf E2 gets induced by mutual induction. (Read Faraday's law of electromagnetic induction.) This mutually induced emf E2 is in phase with E2. If closed circuit is provided at secondary winding, E2 causes current I2 to flow in thecircuit.

For an ideal transformer, E1I1 = E2I2.

EMF equation of the Transformer

Let,N1 = Number of turns in primary windingN2 = Number of turns in secondary windingΦm = Maximum flux in the core (in Wb) = (Bm x A)f = frequency of the AC supply (in Hz)

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As, shown in the fig., the flux rises sinusoidally to its maximum value Φm from 0. It reaches to the maximum value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).Therefore,average rate of change of flux = Φm /(T/4) = Φ

m /(1/4f)Therefore,average rate of change of flux = 4f Φm       ....... (Wb/s).NowInduced emf per turn = rate of change of flux per turnTherefore, average emf per turn = 4f Φm   ..........(Volts).Now, we know,  Form factor = RMS value / average valueTherefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is 1.11

Therefore, RMS value of emf per turn =  1.11 x 4f Φm = 4.44f Φm.

RMS value of induced emf in whole primary winding (E1) = RMS value of emf per turn X Number of turns in primary winding

          E1 = 4.44f N1 Φm          ............................. eq 1

Similarly, RMS induced emf in secondary winding (E2) can be given as

          E2 = 4.44f N2 Φm.          ............................ eq 2

from the above equations 1 and 2,

This is called the emf equation of transformer, which shows, emf / number of turns is same for both primary and secondary winding.

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For an ideal transformer on no load, E1 = V1 and E2 = V2 .where, V1 = supply voltage of primary winding            V2 = terminal voltage of secondary winding

Voltage Transformation Ratio (K)

As derived above,

Where, K = constantThis constant K is known as voltage transformation ratio.

If N2 > N1, i.e. K > 1, then the transformer is called step-up transformer. If N2 < N1, i.e. K < 1, then the transformer is called step-down transformer.

Transformer with resistance and leakage reactance

Magnetic leakage

In a transformer it is observed that, all the flux linked with primary winding does not get linked with secondary winding. A small part of the flux completes its path through air rather than through the core (as shown in the fig at right), and this small part of flux is called as leakage flux or magnetic leakage in transformers. This leakage flux does not link with both the windings, and hence it does not contribute to transfer of energy from primary winding to secondary

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winding. But, it produces self induced emf in each winding. Hence, leakage flux produces an effect equivalent to an inductive coil in series with each winding. And due to this there will be leakage reactance.

(To minimize this leakage reactance, primary and secondary windings are not placed on separate legs, refer the diagram of core type and shell type transformer from construction of transformer.)

Practical Transformer with resistance and leakage reactanceIn the following figure, leakage reactance and resitance of the primary winding as well as secondary winding are taken out, representing a practical transformer.

 Where, R1 and R2 = resistance of primary and secondary winding respectively

              X1 and X2 = leakage reactance of primary and secondary winding resp.

              Z1 and Z2 = Primary impedance and secondary impedance resp. Z1 = R1 + jX1 ...and Z2 = R2 + jX 2 .The impedance in each winding lead to some voltage drop in each winding. Considering this voltage drop the voltage equation of transformer can be given as - V1 = E1 + I1(R1 + jX1 ) --------primary sideV2 = E2 - I2(R2 + jX2 ) --------secondary side

where, V1 = supply voltage of primary winding            V2 = terminal voltage of secondary winding            E1 and E2 = induced emf in primary and secondary winding respectively. (EMF equation of a transformer.)

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UNIT-II

Transformer - Losses and Efficiency

Losses in transformer In any electrical machine, 'loss' can be defined as the difference between input power and

output power. An electrical transformer is an static device, hence mechanical losses (like windage or friction losses) are absent in it. A transformer only consists of electrical losses (iron losses and copper losses). Transformer losses are similar to losses in a DC machine, except that transformers do not have mechanical losses.

Losses in transformer are explained below -

(i) Core losses or Iron losses

Eddy current loss and hysteresis loss depend upon the magnetic properties of the material used for the construction of core. Hence these losses are also known as core losses or iron losses.

Hysteresis loss in transformer: Hysteresis loss is due to reversal of magnetization in the transformer core. This loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value of flux density. It can be given by, Steinmetz formula:Wh= ηBmax

1.6fV (watts)where,   η = Steinmetz hysteresis constant             V = volume of the core in m3

Eddy current loss in transformer: In transformer, AC current is supplied to the primary winding which sets up alternating magnetizing flux. When this flux links with secondary winding, it produces induced emf in it. But some part of this flux also gets linked with other conducting parts like steel core or iron body or the transformer, which will result in induced emf in those parts, causing small circulating current in them. This current is called as eddy current. Due to these eddy currents, some energy will be dissipated in the form of heat.

 (ii) Copper loss in transformer

Copper loss is due to ohmic resistance of the transformer windings.  Copper loss for the primary winding is I1

2R1 and for secondary winding is I22R2. Where, I1 and I2 are current in primary and

secondary winding respectively, R1 and R2 are the resistances of primary and secondary winding respectively. It is clear that Cu loss is proportional to square of the current, and current depends on the load. Hence copper loss in transformer varies with the load.

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Efficiency of TransformerJust like any other electrical machine, efficiency of a transformer can be defined as the output power divided by the input power. That is  efficiency = output / input .

Transformers are the most highly efficient electrical devices. Most of the transformers have full load efficiency between 95% to 98.5% . As a transformer being highly efficient, output and input are having nearly same value, and hence it is impractical to measure the efficiency of transformer by using output / input. A better method to find efficiency of a transformer is using, efficiency = (input - losses) / input = 1 - (losses / input).

Condition for maximum efficiency

Let, Copper loss = I12R1

Iron loss = Wi

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Hence, efficiency of a transformer will be maximum when copper loss and iron losses are equal.That is Copper loss = Iron loss.

All day efficiency of transformer

As we have seen above, ordinary or commercial efficiency of a transformer can be given as

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But in some types of transformers, their performance can not be judged by this efficiency. For example, distribution transformers have their primaries energized all the time. But, their secondaries supply little load all no-load most of the time during day (as residential use of electricity is observed mostly during evening till midnight).That is, when secondaries of transformer are not supplying any load (or supplying only little load), then only core losses of transformer are considerable and copper losses are absent (or very little). Copper losses are considerable only when transformers are loaded. Thus, for such transformers copper losses are relatively less important.  The performance of such transformers is compared on the basis of energy consumed in one day.

All day efficiency of a transformer is always less than ordinary efficiency of it.

Equivalent circuit of Transformer

In a practical transformer - (a) some leakage flux is present at both primary and secondary sides. This leakage gives rise to leakage reactances at both sides, which are denoted as X1 and X2 respectively.(b) Both the primary and secondary winding possesses resistance, denoted as R1 and R2 respectively. These resistances cause voltage drop as, I1R1 and I2R2 and also copper loss I1

2R1 and I2

2R2.(c) Permeability of the core can not be infinite; hence some magnetizing current is needed. Mutual flux also causes core loss in iron parts of the transformer. We need to consider all the above things to derive equivalent circuit of a transformer.

Equivalent circuit of transformer

Resistances and reactances of transformer, which are described above, can be imagined separately from the windings (as shown in the figure below). Hence, the function of windings, thereafter, will only be the transforming the voltage.

The no load current I0 is divided into, pure inductance X0 (taking magnetizing components Iμ) and non induction resistance R0 (taking working component Iw) which are connected into parallel across the primary. The value of E1 can be obtained by subtracting I1Z1 from V1. The value of R0

and X0 can be calculated as, R0 = E1 / Iw and X0 = E1 / Iμ.

But, using this equivalent circuit does not simplifies the calculations. To make calculations simpler, it is preferable to transfer current, voltage and impedance either to primary side or to the secondary side. In that case, we would have to work with only one winding which is more convenient.

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From the voltage transformation ratio, it is clear that,E1 / E2 = N1 / N2 = K

Now, lets refer the parameters of secondary side to primary.Z2 can be referred to primary as Z2'where, Z2' = (N1/N2)2Z2 = K2Z2.   ............where K= N1/N2.that is, R2'+jX2' = K2(R2+jX2)equating real and imaginary parts,R2' =  K2R2 and X2' = K2X2 .And V2' = KV2 The following figure shows the equivalent circuit of transformer with secondary parameters referred to the primary.

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Now, as the values of winding resistance and leakage reactance are so small that, V1 and E1 can be assumed to be equal. Therefore, the exciting current drawn by the parallel combination of  R0 and X0 would not affect significantly, if we move it to the input terminals as shown in the figure below.

Now, let R1 + R2' = R'eq  and X1 + X2' = X'eqThen the equivalent circuit of transformer becomes as shown in the figure below

Approximate equivalent circuit of transformer

If only voltage regulation is to be calculated, then even the whole excitation branch (parallel combination of R0 and X0) can be neglected. Then the equivalent circuit becomes as shown in the figure below

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Open circuit and Short circuit Test on transformer

These two transformer tests are performed to find the parameters of equivalent circuit of transformer and losses of the transformer. Open circuit test and short circuit test on transformer are very economical and convenient because they are performed without actually loading of the transformer.

Open circuit or No load test on TransformerOpen circuit test or no load test on a transformer is performed to determine 'no load loss (core loss)' and 'no load current I0'. The circuit diagram for open circuit test is shown in the figure below.

 Usually high voltage (HV) winding is kept open and the low voltage (LV) winding is connected to its normal supply. A wattmeter (W), ammeter (A) and voltmeter (V) are connected to the LV winding as shown in the figure. Now, applied voltage is slowly increased from zero to normal rated value of the LV side with the help of a variac. When the applied voltage reaches to the rated value of the LV winding, readings from all the three instruments are taken.The ammeter reading gives the no load current I0. As I0 itself is very small, the voltage drops due to this current can be neglected.

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The input power is indicated by the wattmeter (W). But, as the other side of transformer is open circuited, there is no output power. Hence, this input power only consists of core losses and copper losses. But as described above, short circuit current is so small that these copper losses can be neglected. Hence, now the input power is almost equal to the core losses. Thus, the wattmeter reading gives the core losses of the transformer.

Sometimes, a high resistance voltmeter is connected across the HV winding. Though, a voltmeter is connected, HV winding can be treated as open circuit as the current through the voltmeter is negligibly small. This helps in to find voltage transformation ration (K).

The two components of no load current can be given as,Iμ = I0sinΦ0   and    Iw = I0cosΦ0.cosΦ0 (no load power factor) = W / (V1I0). ... (W = wattmeter reading)From this, shunt parameters of equivalent circuit parameters of equivalent circuit of transformer (X0 and R0) can be calculated asX0 = V1/Iμ  and  R0 = V1/Iw.

(These values are referring to LV side of the transformer.)Hence, it is seen that open circuit test gives core losses of transformer and shunt parameters of the equivalent circuit.

Short circuit or Impedance test on Transformer

The connection diagram for short circuit test or impedance test on transformer is as shown in the figure below. The LV side of transformer is short circuited and wattmeter (W), voltmere (V) and ammeter (A) are connected on the HV side of the transformer. Voltage is applied to the HV side and increased from the zero until the ammeter reading equals the rated current. All the readings are taken at this rated current.

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The ammeter reading gives primary equivalent of full load current (Isc).The voltage applied for full load current is very small as compared to rated voltage. Hence, core loss due to small applied voltage can be neglected. Thus, the wattmeter reading can be taken as copper loss in the transformer.Therefore, W = Isc

2Req....... (where Req is the equivalent resistance of transformer) Zeq = Vsc/Isc.Therefore, equivalent reactance of transformer can be calculated from the formula  Zeq

2 = Req2 +

Xeq2.

These, values are referred to the HV side of the transformer.Hence, it is seen that the short circuit test gives copper losses of transformer and approximate equivalent resistance and reactance of the transformer.

Why Transformers are rated in kVA?

From the above transformer tests, it can be seen that Cu loss of a transformer depends on current, and iron loss depends on voltage. Thus, total transformer loss depends on volt-ampere (VA). It does not depend on the phase angle between voltage and current, i.e. transformer loss is independent of load power factor. This is the reason that transformers are rated in kVA.

Sumpner's test or Back-to-Back test on Transformer

Sumpner's test or back to back test on transformer is another method for determining transformer efficiency, voltage regulation and heating under loaded conditions. Short circuit and open circuit tests on transformer can give us parameters of equivalent circuit of transformer, but they can not help us in finding the heating information. Unlike O.C. and S.C. tests, actual loading is simulated in Sumpner's test. Thus the Sumpner's test give more accurate results of regulation and efficiency than O.C. and S.C. tests.

Sumpner's testSumpner's test or back to back test can be employed only when two identical transformers are available. Both transformers are connected to supply such that one transformer is loaded on another. Primaries of the two identical transformers are connected in parallel across a supply. Secondaries are connected in series such that emf's of them are opposite to each other. Another low voltage supply is connected in series with secondaries to get the readings, as shown in the circuit diagram shown below.

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In above diagram, T1 and T2 are identical transformers. Secondaries of them are connected in voltage opposition, i.e. EEF and EGH. Both the emf's cancel each other, as transformers are identical. In this case, as per superposition theorem, no current flows through secondary. And thus the no load test is simulated. The current drawn from V1 is 2I0, where I0 is equal to no load current of each transformer. Thus input power measured by wattmeter W1 is equal to iron losses of both transformers.

i.e. iron loss per transformer Pi = W1/2.

Now, a small voltage V2 is injected into secondary with the help of a low voltage transformer. The voltage V2 is adjusted so that, the rated current I2 flows through the secondary. In this case, both primaries and secondaries carry rated current. Thus short circuit test is simulated and wattmeter W2 shows total full load copper losses of both transformers.

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i.e. copper loss per transformer PCu = W2/2.From above test results, the full load efficiency of each transformer can be given as -

Auto Transformer

  An auto transformer is an electrical transformer having only one winding. The winding has at least three terminals which is explained in the construction details below.

Some of the advantages of auto-transformer are that,

they are smaller in size,  cheap in cost,  low leakage reactance, increased kVA rating,  low exciting current etc. 

An example of application of auto transformer is, using an US electrical equipment rated for 115 V supply (they use 115 V as standard) with higher Indian voltages. Another example could be in starting method of three phase induction motors.

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Construction of auto transformer

 An auto transformer consists of a single copper wire, which is common in both primary as well as secondary circuit. The copper wire is wound a laminated silicon steel core, with at least three tappings taken out. Secondary and primary circuit share the same neutral point of the winding. The construction is well explained in the diagram. Variable turns ratio at secondary can be obtained by the tappings of the winding (as shown in the figure), or by providing a smooth sliding brush over the winding. Primary terminals are fixed.Thus, in an auto transformer, you may say, primary and secondary windings are connected magnetically as well as electrically.

Working of auto transformer

As I have described just above, an auto transformer has only one winding which is shared by both primary and secondary circuit, where number of turns shared by secondary are variable. EMF induced in the winding is proportional to the number of turns. Therefore, the secondary voltage can be varied by just varying secondary number of turns.As winding is common in both circuits, most of the energy is transferred by means of electrical conduction and a small part is transferred through induction.

The considerable disadvantages of an auto transformer are,

any undesirable condition at primary will affect the equipment at secondary (as windings are not electrically isolated),

due to low impedance of auto transformer, secondary short circuit currents are very high, harmonics generated in the connected equipment will be passed to the supply.

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UNIT-III

Three Phase Transformers

Usually power is generated and distributed in three phase system, and therefore it is obvious that we would need three phase transformers to step up and step down voltages. Although, it is practically possible to use three suitably interconnected 'single phase transformers' instead of one 'three phase transformer', the following advantages of three phase transformers  encourage their use -

One 'three phase transformer' occupies less space than a gang of three 'single phase transformers'.

Single 'three phase' unit is more economical The overall bus-bar structure, switchgear and installation of  'three phase transformer' is

simpler.

Construction of three phase transformerThree phase transformers can be of core type or shell type (just like single phase transformers). The constructional details of core type as well as shell type three phase transformers are as follows.

Core type construction

 The construction of a core type three phase transformer is as shown in the figure. The core consists of three legs or limbs. As usual, the core is made up of thin laminated sheets to reduce eddy current losses. Each limb has primary and secondary windings in cylindrical shape (former wound) arranged concentrically. The construction is well illustrated in the figure.

Shell type construction

 In a shell type three phase transformer, three phases are more independent than they are in core type. Each phase has its individual magnetic circuit. The construction of shell type three phase

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transformer is illustrated in the figure at right. The construction is similar to that of three single phase shell type transformers kept on the top of each other.

 The basic working principle of a three phase transformer is similar to the working principle of a single phase transformer. Power from primary is transferred to the secondary by the phenomenon of mutual induction.The main drawback in a three phase transformer is that, even if fault occurs in one phase, the whole transformer is removed from service for repairs.

Three Phase Transformer Connections

Three phase transformer connections In three phase system, the three phases can be connected in either star or delta configuration. In case you are not familiar with those configurations, study the following image which explains star and delta configuration. In any of these configurations, there will be a phase difference of 120° between any two phases.

Three phase transformer connectionsWindings of a three phase transformer can be connected in various configurations as (i) star-star, (ii) delta-delta, (iii) star-delta, (iv) delta-star, (v) open delta and (vi) Scott connection. These configurations are explained below.

Star-star (Y-Y)

Star-star connection is generally used for small, high-voltage transformers. Because of star connection, number of required turns/phase is reduced (as phase voltage in star connection is 1/√3 times of line voltage only). Thus, the amount of insulation required is also reduced.

The ratio of line voltages on the primary side and the secondary side is equal to the transformation ratio of the transformers.

Line voltages on both sides are in phase with each other. This connection can be used only if the connected load is balanced.

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Delta-delta (Δ-Δ)

This connection is generally used for large, low-voltage transformers. Number of required phase/turns is relatively greater than that for star-star connection.

The ratio of line voltages on the primary and the secondary side is equal to the transformation ratio of the transformers. 

This connection can be used even for unbalanced loading.  Another advantage of this type of connection is that even if one transformer is disabled,

system can continue to operate in open delta connection but with reduced available capacity.

Star-delta OR wye-delta (Y-Δ)

The primary winding is star star (Y) connected with grounded neutral and the secondary winding is delta connected. 

This connection is mainly used in step down transformer at the substation end of the transmission line. 

The ratio of secondary to primary line voltage is 1/√3 times the transformation ratio.  There is 30° shift between the primary and secondary line voltages.

Delta-star OR delta-wye (Δ-Y)

The primary winding is connected in delta and the secondary winding is connected in star with neutral grounded. Thus it can be used to provide 3-phase 4-wire service. 

This type of connection is mainly used in step-up transformer at the beginning of transmission line. 

The ratio of secodary to primary line voltage is √3 times the transformation ratio. 

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There is 30° shift between the primary and secondary line voltages. 

Above transformer connection configurations are shown in the following figure.

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Open delta (V-V) connection

Two transformers are used and primary and secondary connections are made as shown in the figure below. Open delta connection can be used when one of the transformers in Δ-Δ bank is disabled and the service is to be continued until the faulty transformer is repaired or replaced. It can also be used for small three phase loads where installation of full three transformer bank is un-necessary. The total load carrying capacity of open delta connection is 57.7% than that would be for delta-delta connection.

Scott (T-T) connection

Two transformers are used in this type of connection. One of the transformers has centre taps on both primary and secondary windings (which is called as main transformer). The other transormer is called as teaser transformer. Scott connection can also be used for three phase to two phase conversion. The connection is made as shown in the figure below.

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Parallel Operation of Transformers

Sometimes, it becomes necessary to connect more than one transformers in parallel, for example, for supplying excess load of the rating of existing transformer. If two or more transformers are connected to a same supply on the primary side and to a same load on the secondary side, then it is called as parallel operation of transformers.

Necessity of Parallel Operation of Transformers

Why parallel operation of transformers is needed?

Increased Load: When load is increased and it exceeds the capacity of existing transformer, another transformer may be connected in parallel with the existing transformer to supply the increased load.

Non-availability of large transformer: If a large transformer is not available which can meet the total requirement of load, two or more small transformers can be connected in parallel to increase the capacity.

Increased reliability: If multiple transformers are running in parallel, and a fault occurs in one transformer, then the other parallel transformers still continue to serve the load. And the faulty transformer can be taken out for the maintenance.

Transportation is easier for small transformers: If installation site is located far away, then transportation of smaller units is easier and may be economical.

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Conditions for Parallel Operation

When two or more transformers are to be operated in parallel, then certain conditions have to be met for proper operation. These conditions are - 

Voltage ratio of all connected transformers must be same.If the voltage ratio is not same, then the secondaries will not show equal voltage even if the primaries are connected to same busbar. This results in a circulating current in secondaries, and hence there will be reflected circulating current on the primary side also. In this case, considerable amount of current is drawn by the transformers even without load.

The per unit (pu) impedance of each transformer on its own base must be same.Sometimes, transformers of different ratings may be required to operate in parallel. For, proper load sharing, voltage drop across each machine must be same. That is, larger transformer has to draw equivalent large current. That is why per unit impedance of the connected transformers must be same.

The polarity of all connected transformers must be same in order to avoid circulating currents in transformers. Polarity of a transformer means the instantaneous direction of induced emf in secondary. If polarity is opposite to each other, huge circulating current flows.

The phase sequence must be identical of all parallel transformers.This condition is relevant to poly-phase transformers only. If the phase sequences are not same, then transformers can not be connected in parallel.

The short-circuit impedances should be approximately equal (as it is very difficult to achieve identical impedances practically).

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UNIT-IV

Three Phase Induction Motor

A three phase induction motor runs on a three phase AC supply. 3 phase induction motors are extensively used for various industrial applications because of their following advantages -

They have very simple and rugged (almost unbreakable) construction they are very reliable and having low cost they have high efficiency and good power factor minimum maintenance required 3 phase induction motor is self starting hence extra starting motor or any special

starting arrangement is not required

They also have some disadvantages

speed decreases with increase in load, just like a DC shunt motor if speed is to be varied, we have sacrifice some of its efficiency

Construction of a 3 phase induction motorJust like any other motor, a 3 phase induction motor also consists of a stator and a rotor. Basically there are two types of 3 phase IM - 1. Squirrel cage induction motor and 2. Phase Wound induction motor (slip-ring induction motor). Both types have similar constructed rotor, but they differ in construction of rotor. This is explained further.

Stator

The stator of a 3 phase IM (Induction Motor) is made up with number of stampings, and these

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stampings are slotted to receive the stator winding. The stator is wound with a 3 phase winding which is fed from a 3 phase supply. It is wound for a defined number of poles, and the number of poles is determined from the required speed. For greater speed, lesser number of poles is used and vice versa. When stator windings are supplied with 3 phase ac supply, they produce alternating flux which revolves with synchronous speed. The synchronous speed is inversely proportional to number of poles (Ns = 120f / P). This revolving or rotating magnetic flux induces current in rotor windings according to Faraday's law of mutual induction.

Rotor

As described earlier, rotor of a 3 phase induction motor can be of either two types, squirrel cage rotor and phase wound rotor (or simply - wound rotor).

Squirrel cage rotor

Most of the induction motors (upto 90%) are of squirrel cage type. Squirrel cage type rotor has very simple and almost indestructible construction. This type of rotor consist of a cylindrical laminated core, having parallel slots on it. These parallel slots carry rotor conductors. In this type of rotor, heavy bars of copper, aluminum or alloys are used as rotor conductors instead of wires.Rotor slots are slightly skewed to achieve following advantages -

1. it reduces locking tendency of the rotor, i.e. the tendency of rotor teeth to remain under stator teeth due to magnetic attraction.

2. increases the effective transformation ratio between stator and rotor

3. increases rotor resistance due to increased length of the rotor conductor

The rotor bars are brazed or electrically welded to short circuiting end rings at both ends. Thus this rotor construction looks like a squirrel cage and hence we call it. The rotor bars are permanently short circuited, hence it is not possible to add any external resistance to armature circuit.

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Phase wound rotor

Phase wound rotor is wound with 3 phase, double layer, distributed winding. The number of poles of rotor are kept same to the number of poles of the stator. The rotor is always wound 3 phase even if the stator is wound two phase.The three phase rotor winding is internally star connected. The other three terminals of the winding are taken out via three insulated sleep rings mounted on the shaft and the brushes resting on them. These three brushes are connected to an external star connected rheostat. This arrangement is done to introduce an external resistance in rotor circuit for starting purposes and for changing the speed / torque characteristics.When motor is running at its rated speed, slip rings are automatically short circuited by means of a metal collar and brushes are lifted above the slip rings to minimize the frictional losses.

Production of rotating magnetic field in polyphase stator

In an induction motor, when AC supply is given to the the stator, magnetic flux is produced which is revolving at synchronous speed. This post will explain you in brief about production of rotating magnetic flux for 2 phase as well as 3 phase supply.

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For 2 phase supply:

fig (a)Let the stator is wound for 2 phase supply. The two phases are kept 90 space degrees apart as illustrated in fig (a).

Let, Φ1 and  Φ2 be the instantaneous values of the fluxes set up by phase 1 and phase 2 respectively.

(i) When θ = 0° (at origin fig. a), magnitude of the flux set up by phase-1 will be 0 and the magnitude of the flux by phase 2 will be maximum but in negative direction. This is illustrated in fig (b). Hence the magnitude of the resultant flux Φr will be equal to Φm.

(ii) θ = 45° (position 1 in fig a)Flux by phase-1 >> Φ1 = sqrt.2 * Φm.Flux by phase-2  >> Φ2 = sqrt.2 * Φm.

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Hence resultant flux >> Φr = Φm.But the resultant has shifted 45 degrees clockwise.

(iii) θ = 90° (position 2)Flux by phase-1 >> Φ1 = Φm.Flux by phase-2  >> Φ2 = 0.Hence resultant flux >> Φr = Φm.But the resultant has further shifted 45 degrees clockwise OR resultant has shifted 90 degrees from its initial position.

(iv) θ = 135° (position 3)Flux by phase-1 >> Φ1 = Φm.Flux by phase-2  >> Φ2 = Φm.Hence resultant flux >> Φr = Φm.But the resultant has further shifted 45 degrees clockwise OR resultant has shifted 135 degrees from its initial position.

(iv) θ = 180° (position 4)Flux by phase-1 >> Φ1 = 0.Flux by phase-2  >> Φ2 = Φm.Hence resultant flux >> Φr = Φm.But the resultant has further shifted 45 degrees clockwise OR resultant has shifted 180 degrees from its initial position.Thus, it can be concluded that the magnitude of the resultant flux remains constant but its direction keeps rotating clockwise.

The speed of the rotating magnetic flux is called as synchronous speed (Ns) and it is given by

where, f =frequency of the supply and  P = number of poles.

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3 Phase supply:

Similarly, for a three phase supply, following figures will illustrate.

Working principle and types of an Induction Motor

Induction Motors are the most commonly used motors in many applications. These are also called as Asynchronous Motors, because an induction motor always runs at a speed lower than synchronous speed. Synchronous speed means the speed of the rotating magnetic field in the stator.

There basically 2 types of induction motor depending upon the type of input supply - (i) Single phase induction motor and (ii) Three phase induction motor.

Or they can be divided according to type of rotor - (i) Squirrel cage motor and (ii) Slip ring motor or wound type

Basic working principle of an Induction Motor

In a DC motor, supply is needed to be given for the stator winding as well  as the rotor winding. But in an induction motor only the stator winding is fed with an AC supply.

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Alternating flux is produced around the stator winding due to AC supply. This alternating flux revolves with synchronous speed. The revolving flux is called as "Rotating Magnetic Field" (RMF).

The relative speed between stator RMF and rotor conductors causes an induced emf in the rotor conductors, according to the Faraday's law of electromagnetic induction. The rotor conductors are short circuited, and hence rotor current is produced due to induced emf. That is why such motors are called as induction motors. 

(This action is same as that occurs in transformers, hence induction motors can be called as rotating transformers.) 

Now, induced current in rotor will also produce alternating flux around it. This rotor flux lags behind the stator flux. The direction of induced rotor current, according to Lenz's law, is such that it will tend to oppose the cause of its production. 

As the cause of production of rotor current is the relative velocity between rotating stator flux and the rotor, the rotor will try to catch up with the stator RMF. Thus the rotor rotates in the same direction as that of stator flux to minimize the relative velocity. However, the rotor never succeeds in catching up the synchronous speed. This is the basic working principle of induction motor of either type, single phase of 3 phase. 

Synchronous speed:

 The rotational speed of the rotating magnetic field is called as synchronous speed.

where, f = frequency of the spply            P = number of poles

Slip:

Rotor tries to catch up the synchronous speed of the stator field, and hence it rotates. But in practice, rotor never succeeds in catching up. If rotor catches up the stator speed, there wont be any relative speed between the stator flux and the rotor, hence no induced rotor current and no torque production to maintain the rotation. However, this won't stop the motor, the rotor will slow down due to lost of torque, the torque will again be exerted due to relative speed. That is why the rotor rotates at speed which is always less the synchronous speed.The difference between the synchronous speed (Ns) and actual speed  (N) of the rotor is called as slip.

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Torque equation of three phase induction motor

Torque of a three phase induction motor is proportional to flux per stator pole, rotor current and the power factor of the rotor.

T ∝  ɸ I2 cosɸ2      OR      T = k ɸ I2 cosɸ2 .where, ɸ = flux per stator pole,            I2 = rotor current at standstill,             ɸ2  = angle between rotor emf and rotor current,             k = a constant.

Now, let E2 = rotor emf at standstillwe know, rotor emf is directly proportional to flux per stator pole, i.e. E2 ∝ ɸ.therefore,  T ∝ E2 I2 cosɸ2        OR      T =k1 E2 I2 cosɸ2.

Starting torque

The torque developed at the instant of starting of a motor is called as starting torque. Starting torque may be greater than running torque in some cases, or it may be lesser.We know, T =k1 E2 I2 cosɸ2.

let, R2 = rotor resistance per phase      X2 = standstill rotor reactance

    then,

Therefore, starting torque can be given as,

The constant k1 = 3 / 2πNs

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 Condition for maximum starting torque

If supply voltage V is kept constant, then flux ɸ and E2 both remains constant. Hence,

Hence, it can be proved that maximum starting torque is obtained when rotor resistance is equal to standstill rotor reactance. i.e. R2

2 + X22 =2R2

2 .

 Torque under running condition

T ∝ ɸ Ir cosɸ2 .where, Er = rotor emf per phase under running condition = sE2.  (s=slip)            Ir = rotor current per phase under running conditionreactance per phase under running condition will be  = sX2

therefore,

 as, ɸ ∝ E2.

Maximum torque under running condition

Torque under running condition is maximum at the value of slip (s) which makes rotor reactance per phase equal to rotor resistance per phase.

Crawling and Cogging in Induction Motors

Crawling and cogging both are particularly related to squirrel cage induction motors.

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Crawling

Sometimes, squirrel cage induction motors exhibits a tendency to run at very slow speeds (as low as one-seventh of their synchronous speed). This phenomenon is called as crawling of an induction motor.

This action is due to the fact that, flux wave produced by a stator winding is not purely sine wave. Instead, it is a complex wave consisting a fundamental wave and odd harmonics like 3rd, 5th, 7th etc. The fundamental wave revolves synchronously at synchronous speed Ns whereas 3rd, 5th, 7th harmonics may rotate in forward or backward direction at Ns/3, Ns/5, Ns/7 speeds respectively. Hence, harmonic torques are also developed in addition with fundamental torque.3rd harmonics are absent in a balanced 3-phase system. Hence 3rdd harmonics do not produce rotating field and torque. The total motor torque now consist three components as: (i) the fundamental torque with synchronous speed Ns, (ii) 5th harmonic torque with synchronous speed Ns/5, (iv) 7th harmonic torque with synchronous speed Ns/7 (provided that higher harmonics are neglected).

Now, 5th harmonic currents will have phase difference of 5 X 120 =  600° =2 X 360 - 120 = -120°. Hence the revolving speed set up will be in reverse direction with speed Ns/5. The small amount of 5th harmonic torque produces breaking action and can be neglected.

The 7th harmonic currents will have phase difference of 7 X 120 = 840° = 2 X 360 +120 = + 120°. Hence they will set up rotating field in forward direction with synchronous speed equal to Ns/7. If we neglect all the higher harmonics, the resultant torque will be equal to sum of fundamental torque and 7th harmonic torque. 7th harmonic torque reaches its maximum positive value just before1/7 th of Ns. If the mechanical load on the shaft involves constant load torque, the torque developed by the motor may fall below this load torque. In this case, motor will not accelerate upto its normal speed, but it will run at a speed which is nearly 1/7th of of its normal speed. This phenomenon is called as crawling in induction motors.

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Cogging (Magnetic locking or teeth locking)

Sometimes, the rotor of a squirrel cage induction motor refuses to start at all, particularly if the supply voltage is low. This happens especially when number of rotor teeth is equal to number of stator teeth, because of magnetic locking between the stator teeth and the rotor teeth. When the rotor teeth and stator teeth face each other, the reluctance of the magnetic path is minimum, that is why the rotor tends to remain fixed. This phenomenon is called cogging or magnetic locking of induction motor.

Double squirrel cage motor

Squirrel cage motors are the most commonly used induction motors, but the main drawback in them is their poor starting torque due to low rotor resistance. (Starting torque is directly proportional to the rotor resistance). But increasing the rotor resistance for improving starting torque is not advisory as it will reduce the efficiency of the motor (due to more copper loss). One can not even add external resistance for starting of purposes, as the rotor bars are permanently short circuited (Construction of a squirrel cage rotor is here). These drawbacks are removed by a double squirrel cage motor, which has high starting torque without sacrificing efficiency.

Construction of double squirrel cage rotor

cross section of double squirrel cage rotorRotor of a double squirrel cage motor has two independent cages on the same rotor. The figure at left shows the cross sectional diagram of a double squirrel cage rotor.Bars of high resistance and low reactance are placed in the outer cage, and bars of low resistance and high reactance are placed in the inner cage. The outer cage has high 'reactance to resistance ratio' whereas, the inner cage has low 'reactance to resistance ratio'.

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Working of double squirrel cage motor

At starting of the motor, frequency of induced emf is high because of large slip (slip = frequency of rotor emf / supply frequency). Hence the reactance of inner cage (2πfL    where, f = frequency of rotor emf) will be very high, increasing its total impedance. Hence at starting most of the current flows through outer cage despite its large resistnace (as total impedance is lower than the inner cage). This will not affect the outer cage because of its low reactance. And because of the large resistance of outer cage starting torque will be large.

As speed of the motor increases, slip decreases, and hence the rotor frequency decreases. In this case, the reactance of inner cage will be low, and most of the current will flow through the inner cage which is having low resistance. Hence giving a good efficiency.

When the double cage motor is running at normal speed, frequency of the rotor emf is so low that the reactance of both cages is negligible. The two cages being connected in parallel, the combined resistance is lower.

The torque speed characteristics of double squirrel cage motor for both the cages are shown in the figure below.  

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UNIT-V

Starting methods of three phase induction motors

An induction motor is similar to a poly-phase transformer whose secondary is short circuited. Thus, at normal supply voltage, like in transformers, the initial current taken by the primary is very large for a short while. Unlike in DC motors, large current at starting is due to the absence of back emf. If an induction motor is directly switched on from the supply, it takes 5 to 7 times its full load current and develops a torque which is only 1.5 to 2.5 times the full load torque. This large starting current produces a large voltage drop in the line, which may affect the operation of other devices connected to the same line. Hence, it is not advisable to start induction motors of higher ratings (generally above 25kW) directly from the mains supply.Various starting methods of induction motors are described below.

Direct-on-line (DOL) starters

Small three phase induction motors can be started direct-on-line, which means that the rated supply is directly applied to the motor. But, as mentioned above, here, the starting current would be very large, usually 5 to 7 times the rated current. The starting torque is likely to be 1.5 to 2.5 times the full load torque. Induction motors can be started directly on-line using a DOL starter which generally consists of a contactor and a motor protection equipment such as a circuit breaker. A DOL starter consists of a coil operated contactor which can be controlled by start and stop push buttons. When the start push button is pressed, the contactor gets energized and it closes all the three phases of the motor to the supply phases at a time. The stop push button de-energizes the contactor and disconnects all the three phases to stop the motor.In order to avoid excessive voltage drop in the supply line due to large starting current, a DOL starter is generally used for motors that are rated below 5kW.

Starting of squirrel cage motorsStarting in-rush current in squirrel cage motors is controlled by applying reduced voltage to the stator. These methods are sometimes called as reduced voltage methods for starting of squirrel cage induction motors. For this purpose, following methods are used:

1. By using primary resistors2. Autotransformer3. Star-delta switches4. 1. Using primary resistors:

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Obviously, the purpose of primary resistors is to drop some voltage and apply a reduced voltage to the stator. Consider, the starting voltage is reduced by 50%. Then according to the Ohm's law (V=I/Z), the starting current will also be reduced by the same percentage. From the torque equation of a three phase induction motor, the starting torque is approximately proportional to the square of the applied voltage. That means, if the applied voltage is 50% of the rated value, the starting torque will be only 25% of its normal voltage value. This method is generally used for a smooth starting of small induction motors. It is not recommended to use primary resistors type of starting method for motors with high starting torque requirements.

Resistors are generally selected so that 70% of the rated voltage can be applied to the motor. At the time of starting, full resistance is connected in the series with the stator winding and it is gradually decreased as the motor speeds up. When the motor reaches an appropriate speed, the resistances are disconnected from the circuit and the stator phases are directly connected to the supply lines.

2. Auto-transformers:

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Auto-transformers are also known as auto-starters. They can be used for both star connected or delta connected squirrel cage motors. It is basically a three phase step down transformer with different taps provided that permit the user to start the motor at, say, 50%, 65% or 80% of line voltage. With auto-transformer starting, the current drawn from supply line is always less than the motor current by an amount equal to the transformation ratio. For example, when a motor is started on a 65% tap, the applied voltage to the motor will be 65% of the line voltage and the applied current will be 65% of the line voltage starting value, while the line current will be 65% of 65% (i.e. 42%) of the line voltage starting value. This difference between the line current and the motor current is due to transformer action. The internal connections of an auto-starter are as shown in the figure. At starting, switch is at "start" position, and a reduced voltage (which is selected using a tap) is applied across the stator. When the motor gathers an appropriate speed, say upto 80% of its rated speed, the auto-transformer automatically gets disconnected from the circuit as the switch goes to "run" position.

The switch changing the connection from start to run position may be air-break (small motors) or oil-immersed (large motors) type. There are also provisions for no-voltage and overload, with time delay circuits on an autostarter.

3. Star-delta starter:

This method is used in the motors, which are designed to run on delta connected stator. A two way switch is used to connect the stator winding in star while starting and in delta while running at normal speed. When the stator winding is star connected, voltage over each phase in motor will be reduced by a factor 1/(sqrt. 3) of that would be for delta connected winding. The starting torque will 1/3 times that it will be for delta connected winding. Hence a star-delta starter is equivalent to an auto-transformer of ratio 1/(sqrt. 3) or 58% reduced voltage.

Starting of slip-ring motors

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Slip-ring motors are started with full line voltage, as external resistance can be easily added in the rotor circuit with the help of slip-rings. A star connected rheostat is connected in series with the rotor via slip-rings as shown in the fig. Introducing resistance in rotor current will decrease the starting current in rotor (and, hence, in stator). Also, it improves power factor and the torque is increased. The connected rheostat may be hand-operated or automatic.

As, introduction of additional resistance in rotor improves the starting torque, slip-ring motors can be started on load.The external resistance introduced is only for starting purposes, and is gradually cut out as the motor gathers the speed.

Speed control methods of induction motor

An induction motor is practically a constant speed motor, that means, for the entire loading range, change in speed of the motor is quite small. Speed of a DC shunt motor can be varied very easily with good efficiency, but in case of Induction motors, speed reduction is accompanied by a corresponding loss of efficiency and poor power factor. As induction motors are widely being used, their speed control may be required in many applications. Different speed control methods of induction motor are explained below.

Induction motor speed control from stator side

1. By changing the applied voltage:

From the torque equation of induction motor,

Rotor resistance R2 is constant and if slip s is small then (sX2)2 is so small that it can be neglected. Therefore, T ∝ sE2

2 where E2 is rotor induced emf and E2 ∝ VThus, T ∝ sV2,  which means, if supplied voltage is decreased, the developed torque decreases. Hence, for providing the same load torque, the slip increases with decrease in voltage, and consequently, the speed decreases. This method is the easiest and cheapest, still rarely used, because

1. large change in supply voltage is required for relatively small change in speed.2. large change in supply voltage will result in a large change in flux density, hence, this

will disturb the magnetic conditions of the motor.

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2. By changing the applied frequency

Synchronous speed of the rotating magnetic field of an induction motor is given by,

where, f = frequency of the supply and P = number of stator poles.Hence, the synchronous speed changes with change in supply frequency. Actual speed of an induction motor is given as N = Ns (1 - s). However, this method is not widely used. It may be used where, the induction motor is supplied by a dedicated generator (so that frequency can be easily varied by changing the speed of prime mover). Also, at lower frequency, the motor current may become too high due to decreased reactance. And if the frequency is increased beyond the rated value, the maximum torque developed falls while the speed rises.

3. Constant V/F control of induction motorThis is the most popular method for controlling the speed of an induction motor. As in above method, if the supply frequency is reduced keeping the rated supply voltage, the air gap flux will tend to saturate. This will cause excessive stator current and distortion of the stator flux wave. Therefore, the stator voltage should also be reduced in proportional to the frequency so as to maintain the air-gap flux constant. The magnitude of the stator flux is proportional to the ratio of the stator voltage and the frequency. Hence, if the ratio of voltage to frequency is kept constant, the flux remains constant. Also, by keeping V/F constant, the developed torque remains approximately constant. This method gives higher run-time efficiency. Therefore, majority of AC speed drives employ constant V/F method (or variable voltage, variable frequency method) for the speed control. Along with wide range of speed control, this method also offers 'soft start' capability.

4. Changing the number of stator poles

From the above equation of synchronous speed, it can be seen that synchronous speed (and hence, running speed) can be changed by changing the number of stator poles. This method is generally used for squirrel cage induction motors, as squirrel cage rotor adapts itself for any number of stator poles. Change in stator poles is achieved by two or more independent stator windings wound for different number of poles in same slots.

For example, a stator is wound with two 3phase windings, one for 4 poles and other for 6 poles.

for supply frequency of 50 Hzi) synchronous speed when 4 pole winding is connected, Ns = 120*50/4 = 1500 RPMii) synchronous speed when 6 pole winding is connected, Ns = 120*50/6 = 1000 RPM

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Speed control from rotor side:

1. Rotor rheostat control

This method is similar to that of armature rheostat control of DC shunt motor. But this method is only applicable to slip ring motors, as addition of external resistance in the rotor of squirrel cage motors is not possible.

2. Cascade operation

In this method of speed control, two motors are used. Both are mounted on a same shaft so that both run at same speed. One motor is fed from a 3phase supply and the other motor is fed from the induced emf in first motor via slip-rings. The arrangement is as shown in following figure.

Motor A is called the main motor and motor B is called the auxiliary motor.Let, Ns1 = frequency of motor A       Ns2 = frequency of motor B       P1 = number of poles stator of motor A       P2 = number of stator poles of motor B       N = speed of the set and same for both motors       f = frequency of the supply

Now, slip of motor A, S1 = (Ns1 - N) / Ns1.frequency of the rotor induced emf in motor A,   f1 = S1fNow, auxiliary motor B is supplied with the rotor induce emf

therefore,  Ns2 = (120f1) / P2  =  (120S1f) / P2.

now putting the value of  S1 = (Ns1 - N) / Ns1

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 At no load, speed of the auxiliary rotor is almost same as its synchronous speed.i.e. N = Ns2.from the above equations, it can be obtained that

With this method, four different speeds can be obtained1. when only motor A works, corresponding speed = .Ns1 = 120f / P1

2. when only motor B works, corresponding speed = Ns2 = 120f / P2

3. if commulative cascading is done, speed of the set = N = 120f / (P1 + P2)4. if differential cascading is done, speed of the set = N = 120f (P1 - P2)

3. By injecting EMF in rotor circuit

In this method, speed of an induction motor is controlled by injecting a voltage in rotor circuit. It is necessary that voltage (emf) being injected must have same frequency as of the slip frequency. However, there is no restriction to the phase of injected emf. If we inject emf which is in opposite phase with the rotor induced emf, rotor resistance will be increased. If we inject emf which is in phase with the rotor induced emf, rotor resistance will decrease. Thus, by changing the phase of injected emf, speed can be controlled. The main advantage of this method is a wide rage of speed control (above normal as well as below normal) can be achieved. The emf can be injected by various methods such as Kramer system, Scherbius system etc.

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