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Transformer
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Current Transformer,Potential Transformer Working | Instrument Transformers

Instrument Transformers

Definition of Instrument Transformer

In heavy currents and high voltage a.c. circuits, the measurement can not be done by using the method of extension of ranges of low range meters by providing suitable shunts. In such conditions, specially constructed accurate ratio transformers called instrument transformers. These can he used, irrespective of the voltage and current ratings of the a.c. circuits. These transformers not only extend the range of the low range instruments but also isolate them from high current and high voltage a.c. circuits. This makes their handling very safe. These are generally classified as

(i) current transformers and (ii) potential transformers.

Current Transformers (C.T.) Construction: 

The large alternating currents which can not be sensed or passed through normal ammeters and current coils of watt meters, energy meters can easily be measured by use of current transformers along with normal low range instruments.

A transformer is a device which consists of two winding's called primary and secondary. It transfers energy from one side to another with suitable change in the level of current or voltage. A current transformer basically has a primary coil of one or more turns of heavy cross-sectional area. In some, the bar carrying high current may act as a primary. This is connected in series with the line carrying high current.

The secondary of the transformer is made up of a large number of turns of fine wire having small cross-sectional area. This is usually rated for 5 A. This is connected to the coil of normal range ammeter. Through this ammeter we can note down the value of current flowing through the secondary winding of current transformer. Symbolic representation of a current transformer is as shown in the figure.

Working of a current transformer and C.T Ratio:

A combination of current transformer and ammeter helps us to find out the higher values of current flowing through line. As discussed we step down the value of line current by increasing the turns in secondary winding. This shows that there is inverse relation between between primary and secondary current and the number of turns of primary and secondary. We connect an ammeter to the secondary winding of current transformer to get secondary current which is shown in the following figure.


So now we can calculate the value of current through line or primary current from the C.T ratio. 

Where,
 Np is number turns of primary winding.
 Ns is number turns of secondary winding.
 Ip is current through primary winding.
 Is is current through secondary winding.

Potential Transformers (P.T) Construction:


The large alternating currents which can not be sensed or passed through normal voltmeters and voltage coils of watt meters, energy meters can easily be measured by use of potential transformers along with normal low range instruments.

A potential transformer has two winding's namely primary and secondary. Primary winding has large number of turns and it is connected in parallel to the line(between line and ground) whose voltage is to be measured. Now the secondary has less number of turns. This is usually rated to 110 V and is connected directly to voltmeter. Through this voltmeter we can note down the value of voltage across the secondary winding of potential transformer.Symbolic representation of a potential transformer is as shown in the figure.

Working of a potential transformer and P.T Ratio:

A combination of potential transformer and voltmeter helps us to find out the higher values of potential across the line. As discussed we step down the value of primary voltage by decreasing the turns in secondary winding. This shows that primary and secondary voltage and the number of turns of primary and secondary are directly proportional.We connect an voltmeter across the secondary winding of potential transformer to get secondary voltage which is shown in the following figure.


So we can calculate the value of line voltage or voltage across the primary of potential transformer from the P.T ratio
Where,
 Np is number turns of primary winding.
 Ns is number turns of secondary winding.
 Ip is current through primary winding.
 Is is current through secondary winding.

In this post we have learnt about instrument transformers namely current transformer and potential transformer.

To download this post on instrument transformers as PDF click here


 
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Welding Transformer Working Principle and Applications

Welding Transformer Working Principle and Applications &characteristics of welding transformer

Now a days we have many ac power supplies. So the usage of welding transformer has significant role in welding compared to a motor generator set. When we need to use a motor generator set for welding we need to run it continuously which produces a lot of noise. With the help of welding transformer weld is done with a less noise. Now let us see in detail about welding transformer.

Construction of welding transformer:

1. Welding transformer is a step down transformer.

2. It has a magnetic core with primary winding which is thin and has large number of turns on one arm.

3. A secondary winding with less number of turns and high cross-sectional area on the other arm.

4. Due to this type of windings in primary and secondary it behaves as step down transformer.

5. So we get less voltage and high current from the secondary winding output. This is the construction of ac welding transformer. 

6.A dc welding transformer also has same type of winding the only difference is that we connect a rectifier(which converts ac to dc) at the secondary to get dc output. 

7.We also connect a inductor or filter to smooth the dc current. This will be construction of dc welding transformer. The diagrams are shown below.


Fig 1.DC welding transformer




Fig 2.AC welding transformer

Note:

Many people have a doubt which is primary winding and which is secondary winding. The winding which is connected to power supply is called primary winding and the winding to which load is connected is called secondary winding.

Working of welding transformer:

1.As it is a step down transformer we have less voltage at secondary which is nearly 15 to 45 volts and has high current values which is nearly 200 A to 600 A it can also be higher than this value.

2. For adjusting the voltage on secondary side there are tappings on secondary winding by this we can get required amount of secondary current for welding.

3. These tappings are connected to several high current switches.

4. Now one end of secondary winding is connected to the welding electrode and the other end is connected to the welding pieces as shown in fig 2. 

5.When a high current flows a large amount of  I2R heat is produced due to contact resistance between welding pieces and electrode. 

6.Because of this high heat the tip of electrode melts and fills the gap between the welding pieces.

This is how a welding transformer works.

Volt - ampere characteristics of welding transformer:

Figure given below shows the volt - ampere characteristics of welding transformer.

Arc control of welding transformer:

The impedance of welding transformer must be higher than the normal transformer to control arc and also to control current. 

We can use different reactors for controlling the arc. They are

1.Tapped reactor.

2.Moving coil reactor.

3.Magnetic shunt reactor.

4. Continuously variable reactor.

5. Saturable Reactor.

Now let us see each of this methods for arc control of welding transformer in detail.

1.Tapped reactor:

Below is the circuit for arc control using tapped reactor is given below.

  
With the help of taps we control the current. It has limited current control.

2. Moving coil reactor:

Below is the circuit for arc control using moving coil reactor.





The distance between primary and secondary decides the amount of current. If the distance between the primary and secondary is high then the current is less.

3. Magnetic shunt reactor:

Below is the circuit for arc control using magnetic shunt reactor.
By adjusting the central magnetic shunt flux is changed. By changing the flux current can be changed.

4. Continuously variable reactor:

Below is the circuit for arc control using continuously variable reactor.



By varying the height of reactor core insertion is changed. If core insertion is greater reactance is higher so output current will be less.

5. Saturable reactor:

Below is the circuit for arc control using saturable reactor.

The reactance of the reactor in this is adjusted by changing the value of d.c. excitation which is obtained from d.c. controlled transducer. Higher the d.c. currents, reactor approaches to saturation. This changes the reactance of reactor. By changing the reactance current can be changed.

By using above reactors current can be controlled which helps to control the arc.

In this post we have learnt about welding transformers.

To download this post on welding transformers as PDF click here.

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welding transformer and its characteristics
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Watch A Video On Welding Transformer Working:

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Voltage Regulation of Transformer

Voltage Regulation Of Transformer

Hello everyone,
In this post we are going to discuss about Voltage regulation of a transformer.

Read here : Differences Between Core And Shell Type Transformers

What is meant my Voltage regulation of transformer?
Voltage regulation of a transformer may be defined as the difference between no load voltage of the secondary terminal of a transformer and full load voltage of the secondary terminal of that transformer at a certain power factor. Voltage regulation of a transformer is expressed in percentage of either no load secondary terminal voltage or full load secondary terminal voltage.

Read here : EMF Equation of Transformer & Voltage Transformation Ratio

Objective to calculate voltage regulation of transformer:

Calculating voltage regulation of transformer gives how much efficiently the transformer is resisting the voltage changes from no load to full load. If there is no change in value of secondary voltage from no load to full load then the transformer is ideal and has voltage regulation 0%. So the lower the value of voltage regulation the higher is the performance of the transformer. 

 Procedure to calculate voltage regulation of transformer:

Consider a transformer which is at no load which means the secondary of the transformer is open circuited. In this case the secondary voltage of the transformer and induced emf are same let it be E2 . Now full load is connected to the secondary of a transformer. In this case current I2 passes in the secondary which will lead to voltage drop and is given by I2Z2. Where Z2 is called secondary impedance of transformer. During this situation primary winding will draw equivalent full load current. Because of the voltage drop the secondary voltage cannot be E2 anymore so secondary induced emf will be V2.

Equivalent circuit for calculating voltage regulation of transformer:



Equation for calculating voltage regulation of a transformer:


Voltage regulation of transformer in percentage can be represented as:

Voltage regulation % = (E2-V2/V2)×100%. This is called regulation down. Power factor is specific.

Calculating voltage regulation of transformer for lagging power factor:

Now lets derive the expression for calculating voltage regulation of transformer for lagging power factor.

Phasor diagram:



here cos𝚹2 is lagging power factor

From diagram,

                       OC = OA + AB + BC
                       
                       OA = V2
                       
                       AB = AEcos𝚹=  I2R2cos𝚹2
          
                       BC=DEsin𝚹2=I2R2sin𝚹2

Angle between OC and OD is very less so OC is approximately equal to OD.

                 E2 = OC = OA + AB + BC.

                 E= OC = V2 + I2R2cos𝚹2 + I2R2sin𝚹2

Now voltage regulation of transformer at lagging power factor is,
Voltage regulation% = (E2-V2/V2) × 100%

Voltage regulation%=( I2R2cos𝚹2I2R2sin𝚹2V2 ) ×100%.

Calculating voltage regulation of transformer for leading power factor:

Now lets derive the expression for calculating voltage regulation of transformer for leading power factor.

Phasor diagram:




here cos𝚹is leading power factor
From diagram,

                         OC = OA + AB - BC

                          OA = V2
                       
                         AB = AEcos𝚹2 = I2R2cos𝚹2
          
                         BC = DEsin𝚹2 = I2R2sin𝚹2  

Angle between OC and OD is very less so OC is approximately equal to OD.

                         E2  = OC = OA +AB - BC.

                          E= OC = V2 + I2R2cos𝚹2 - I2R2sin𝚹2

Now voltage regulation of transformer at leading power factor is,
Voltage regulation% = (E2-V2/V2) × 100%

Voltage regulation%=(I2 R2cos𝚹2 - I2R2sin𝚹2 /V2 ) ×100%.

Thus we have learnt what is voltage regulation of transformer and derived expressions for voltage regulation of transformer for lagging and leading power factors. 
You can download this article of Voltage Regulation OF Transformer as a PDF here.
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All Day Efficiency of Transformer/ Distribution Transformer All Day Efficiency

All Day Efficiency of Transformer/ Distribution Transformer All Day Efficiency

In our previous articles we have discussed transformer working,construction etc.Today we discuss one of the important parameter of distribution transformer I.e, "all day efficiency of a distribution transformer".We know for a transformer, the efficiency is defined as the ratio of output power to input power.

Transformer Efficiency= Output Power /Input Power 

The above equation is efficiency of any transformer. But for some special types of transformers such as distribution transformers power efficiency is not the true measure of the performance.For that purpose distribution transformer we calculate all day efficiency.Distribution transformer serve residential and commercial loads.


The load on distribution transformers vary considerably during the period of the day. For most period of the day these transformers are working at 30 to 40 % of full load only or even less than that. But the primary of such transformers is energised at its rated voltage for 24 hours, to provide continuous supply to the consumer.

The core loss which depends on voltage, takes place continuously for all the loads. But copper loss depends on the load condition. For no load, copper loss is negligibly small while on full load it is at its rated value. Hence power efficiency can not give the measure of true efficiency of distribution transformers. in such transformers, the energy output is calculated in kilo watt hour (kWh). Then ratio of total energy output to total energy input (output + losses) is calculated. Such ratio is called energy efficiency or All Day Efficiency of a transformer.

Based on this efficiency, the performance of various distribution transformers is compared. All day efficiency is defined as,


While calculating energies, all energies can be expressed in watt hour (Wh) instead of kilo watt hour (kWh). Such distribution transformers are designed to have very low core losses. This is achieved by limiting the core flux density to lower value by using a relative higher core cross-section i.e. larger iron to copper weight ratio.

The maximum efficiency in distribution transformers occurs at about 60-70 % of the full load. So by proper designing, high energy efficiencies can be achieved for distribution transformers. Numerical problems on all day efficiency of a transformer will be posted soon.

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Cooling Methods of A Transformer

 Power Transformer Cooling Methods 

The transformers get heated due to iron and copper looses occurring in them. It is necessary to dissipate this heat so that the temperature of the windings is kept below the value at which the insulation begins to deteriorate. The cooling of transformer is more difficult than that of rotating machines because the rotating machines create a turbulent airflow which assists in removing the heat generated due to losses. Luckily the losses in transformers are comparatively small. Nevertheless the elaborate cooling arrangements have been devised to deal with the whole range of sizes.

Types of transformer cooling methods:

As far as cooling methods are concerned. the transformers are of following two types

1. Dry type. 2. Oil immersed type.

Dry Type Transformers. Small transformers up to 25 KVA size are of the dry type and have the following cooling arrangements:

(i) Air natural. In this method the natural circulation of surrounding air is utilized to carry away the heat generated by losses. A sheet metal enclosure protects the winding from mechanical injury.

(ii) Air blast. Here the transformer is cooled by a continuous blast of cool air forced through the core and windings . The blast is produced by a fan. The air supply must be filtered to prevent accumulation of dust in ventilating ducts.

Oil Immersed Transformers. In general most transformers are of oil immersed types. The oil provides better insulation than air and it is a better conductor of heat than air. Mineral oil is used for this purpose.Oil immersed transformers are classified as follows:

i) Oil immersed self-cooled transformer. The transformer is immersed in oil and heat generated in cores and windings is passed to oil by conduction. Oil in contact with heated parts rises and its place is taken by cool oil from the bottom. The natural oil transfer: its heat to the tank walls from where heat is taken away by the ambient air. The oil gets cooler and falls to the bottom from where it is dissipated into the surroundings. The tank mince is the best dissipate of heat but a plain tank will have to be excessively large, if used without any auxiliary means for high rating transformers. As both space and oil are costly, these auxiliary means should not increase the cubic capacity of the tank. 
The heat dissipating capacity can be increased by providing (i) corrugations. (ii) fins (iii) tubes and (iv) radiator tanks.


The advantages of ‘oil natural' cooling is that it does not clog the ducts and the windings are fire from effect of moisture.

(ii) Oil immersed forced air-cooled transformers. In this type of cooling, air is directed over the outer surfaces of the tank of the transformer immersed in oil.

(iii) Oil immersed water-cooled transformers. Heat is extracted from the oil by means of a stream of water pumped through a metallic coil immersed in the oil just below the top of the tank.The heated water is in turn cooled in a spray pond or a cooling tower.

(iv) Oil immersed forced oil cooled transformers. In such transformers heat is extracted from the oil by pumping the oil itself upward through the winding and then back by way of external radiators which may themselves be cooled by fans. The extra cost of oil pumping equipment must of course economically justified but it has incidentally the advantage of reducing the temperature difference between top and bottom of enclosing tank. 

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Differences Between Core And Shell Type Transformers - Types of Transformers

What Are The Differences Between Core  And Shell Type Transformers 

In our previous articles we have discusses about differences between lap,wave winding this tutorial we are sharing major differences between core type transformer and shell type transformer. In this tutorial comparisons between shell type and core type transformers are discussed.There are two major types of transformers based on construction.
They are,
1.Core Type Transformers
2.Shell Type Transformers

Types of Transformers

Difference Between Shell And Core Type Transformers

Core Type TransformersShell Type Transformers
1. In core type transformer winding is placed on
two core limbs.
1. In shell type transformer winding is placed on mid arm
of the core.It is installed on mid-limb of the core.
Other limbs will be used as mechanical supporting
2. Core type transformers have only one magnetic flux path.2. Shell type transformers have two magnetic flux path.
3. It has better cooling since more surface is exposed to
atmosphere.
3. Cooling is not effective in shell type when compared
to core type transformer.
4. It is very useful when we need large size low voltage.4. It is very useful when we need small size high voltage.
5. In core type transformer output is less. Because of losses.
So efficiency will be less than shell type transformer.
5. In core type transformer output is high. Because of
less losses.So efficiency will be more.
6. The winding is surrounded considerable part of core.6. Core is surrounded considerable part of winding of
transformer.
7. It has less mechanical protection to coil.7. It has better mechanical protection to coil.
8. Core has two limbs.8. Core has three limbs.
9. This transformer is easy to repair,Easy to maintain.9. This transformer is not easy to repair.We need a
skilled technician to maintain this type of transformer.
10. In this type transformer concentric cylindrical
winding are used
10. In this type transformer sandwiched winding are used.

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Parallel Operation of Transformers

The transformers are connected in parallel when the load on them is more than the rating of the individual transformers. Before going to discuss about parallel operation of single phase transformers  A small question for you all that is 'why parallel operation of transformers is required?'.Answer is simple we have some advantages over operating single transformer units so we go for parallel operation of transformers.
Parallel Operation of Transformers

Advantages of Parallel Operation of Transformers

Parallel operation is nothing but connecting primary windings of two or more transformers to supply and secondary windings to common loads.To supply more than  the rating of existing transformer parallel connections will be employed.It is very economical to operate small no.of transformer units in parallel to supply rated output than a big rated transformer.

Parallel operation of transformer because of following advantages 

  1. Maximum power system efficiency: Power system loads always varies to maintain its efficiency we operate transformers in parallel because transformer gives the maximum efficiency at full load,if we use single large transformer,load on the large transformer always varies so it will operate with low efficiency. In other hand if we operate small units in parallel we can switch on/off as per load demand and we can maintain high efficiency.
  2. Ease of electrical power switching: Scheduling the power with single large transformer will become difficult because of it's high rating and distribution system will be connected ,controlled by a single transformer we can avoid this problem using parallel operation of transformers.This also improves power system reliability,flexibility.
  3. Economical Issues /Non-availability of large transformer: If a large transformer of required rating is unavailable we can go for small rated transformers which can perform better than single large unit. And large transformer operating costs will be more than parallel operation of single phase transformers.
  4. Easier transportation: Transportation will be very easy for small transformers: If installation location is far away from transformer manufacturing/selling point.So parallel operation of transformers is to be encouraged. 

Conditions for Parallel Operation of Transformers

We can't connect any two or more transformers in parallel blindly.When two or more transformers need to operate in parallel, they must met some conditions for efficient performance.Major conditions for parallel operation of transformers are listed below.
  • The voltage ratings and voltage ratios of the transformers should be the same.
  • Transformers should be properly connected with regard to their polarities.
  • The per unit or percentage impedance of the transformers should be equal.
  • The reactance/resistance ratios of the transformers should be the same.

Same Voltage Rating and Voltage Ratio

The voltage ratios of two transformers must be same but why?
Reason is simple if voltage ratio of two transformers is different  and they put  in parallel with same primary supply voltage, there will be a difference in secondary voltages. As secondaries of transformers completes a closed loop there will be circulating  currents.In this case, considerable amount of current is drawn by the transformers even without load.As the internal impedance of transformer is small, a small voltage difference may cause sufficiently high circulating  current  causing unnecessary extra I²R loss.
Parallel Operation of Transformers
Circulating Currents=IC= (EA-EB)/ZA+ZB

Connections with regard to Polarity

Polarity of all connected transformers must be same in order to avoid short circuit.Polarity of a transformer taken w.r.t dot notation.Dots of all transformers connected together on primary and secondary separately. If polarity is opposite to each other, huge circulating current flows.In the below diagram right and wrong parallel operation connections are shown take a look.
Parallel Operation of Transformers


The phase sequence must be identical of all parallel transformers.

This condition is can be applied only to poly-phase transformers. If the phase sequences are not same, then transformers can not be connected in parallel.During the cycle, each pair of phases will be short circuited.

Equal Percentage Impedance

The per unit (pu) impedance of each transformer on its own base must be same.This condition is also desirable for proper parallel operation of single phase  transformers. If this condition is not met, the transformers will not share the load according to their kVA ratings.

Sometimes this condition is not fulfilled by the design of the transformers. In that case, it can be corrected by inserting proper amount of resistance or reactance or both in series with either primary or secondary circuits of the transformers where the impedance is below the value required to fulfill this condition.That is why per unit impedance of the connected transformers must be same.

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Open and Short Circuit Test on Transformer

We conduct open circuit and short circuit test on single phase transformer to determine the  efficiency and regulation of a transformer on any load condition and at any power factor.Open circuit & short circuit test are also called as OC test & SC test on transformer.This method of finding the parameters of a transformer is called as an indirect loading method.

Open Circuit(OC) and Short Circuit(SC) Test on Transformer

What is the need of OC & SC test on transformers?

Open circuit test and short circuit test on transformer are very economical and convenient because they are performed without actually loading of the transformer.because they furnish the required information without actually loading the transformer. In fact, the testing of very large a.c. machinery consists of running two tests similar to the open and short-circuit tests of a transformer.
Open-circuit or No-load Test On Single Phase Transformers

The circuit diagram for open circuit test is shown in the figure. A voltmeter(V), wattmeter(W), and an ammeter(A) are connected in LV side of the transformer.Usually high voltage (HV) winding is kept open and the low voltage (LV) winding is connected to its normal supply.Because we are going to find the max output voltage of transformer which is present at HV side.This is the reason why HV winding is open circuited.

Procedure of Open Circuit(OC) Test

  1. Switch on single phase AC supply,with the help of variac,increase the voltage until the voltmeter raeds the rated voltage of the LV side.
  2. At the instant of  rated LV voltage, Note down the readings of all three instruments.(Voltmeter, Ammeter and Wattmeter readings) are recorded.

The ammeter reading gives the no load current I0.As no load current (I0) very small,voltage drop due to this current also neglected.The input power supplied to the transformer is indicated by the watt meter (W).Output power of transformer in open circuit test is zero because  other side of transformer is open circuited.That means input supply is to just compensate the  core losses and copper losses.By neglecting some voltage drop due to small no-load current,Watt meter (W) reading gives the core losses of the transformer.

 Here,Wo = Pi  = Iron losses
       Calculations : We know that,
             Wo = VoIo cos Φ(watt meter reading)
             cos Φo = Wo /(VoIo) = no load power factor
Once cos Φo is known we can obtain,
              Ic  = Io cos Φo 
 and        Im = Io sin Φo
       Once Ic  and Im are known we can determine exciting circuit parameters as,
              Ro = Vo /Ic   Ω 
          Xo = Vo /Im   Ω


where, X0,R0 are equivalent exciting reactance,resistance of transformer.

Key Point : We should use LPF (low power factor)watt meter to get error free results.Beacuse cos Φo is very low in the above case.The above values are calculated by taking LV side of transformer as reference.If the meters are connected on secondary and primary is kept open then from O.C. test we get Ro' and Xo' with which we can obtain Ro and Xo knowing the transformation ratio K.
The equivalent circuit derived by the OC test is shown below.

Hence,we can conclude that open circuit test on transformer gives 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 on transformer is shown in the figure. A voltmeter(V), wattmeter(W), and an ammeter(A) are connected in HV side of the transformer as shown.The secondary winding is short circuited with the help of thick copper wire or solid link. As high voltage side is always low current side, it is convenient to connect high voltage side to supply and shorting the low voltage side.

Procedure of Short Circuit (OC) Test


  1. Apply voltage to HV side.
  2. Increase the voltage from the zero until the ammeter reading equals the rated current.
  3. At the instant of  rated HV current, Note down the readings of all three instruments.(Voltmeter, Ammeter and wattmeter readings) are recorded.

Now the current flowing through the windings of transformer is rated current. Hence the total copper loss will be full load copper loss.Iron losses are neglected due to small fraction of voltage supllied. Hence the wattmeter reading shows the power loss which is equal to full load copper losses as iron losses are neglected.

Wsc = (Pcu) F.L. = Full load copper loss
      Calculations : From S.C. test readings we can write,
              Wsc = Vsc Isc cos Φsc
...            cos Φsc = Vsc Isc /Wsc = short circuit power factor
               Wsc = Isc2 R1e = copper loss
...             R1e =Wsc /Isc2
while        Z1e =Vsc /Isc = √(R1e2 + X1e2)
                X1e = √(Z1e2 - R1e2)

Thus we get the equivalent circuit parameters R1e, X1e and Z1e. Knowing the transformation ratio K, the equivalent circuit parameters referred to secondary also can be obtained.

We conduct open circuit and short circuit test on single phase transformer to determine the  efficiency and regulation of a transformer on any load condition and at any power factor.Open circuit & short circuit test are also called as OC test & SC test on transformer.This method of finding the parameters of a transformer is called as an indirect loading method.

Calculation of Efficiency of transformer from O.C. and S.C. Tests

Efficiency, η = Power output in KW/ Power input in KW

= Power output in KW/ (Power output in KW + Losses)

= Power output in KW/ (Power output in KW + Copper loss + Core loss)

Consider that the KVA rating of the transformer is S, a fraction of the load is x and the power factor of the load is Cos Φ. Then
The output power in KW = xSCos Φ
Suppose the copper loss at full load is Pcu (since x =1),
Then copper loss at x per unit loading = x2Pcu
Therefore the efficiency of the transformer is
Efficiency, η = xSCos Φ / (xS Cos Φ + x2 Pxcu + Pxcore)
In the above efficiency equation, the core or iron losses and full load copper losses are found by OC and SC tests.

Calculation of Regulation

Percentage voltage regulation, %R = ((E2 – V2)/ V2 )×100
The expression of voltage regulation in terms voltage drops is given as
%R = ((I1R01 cos Φ +/- I1X01 sin Φ) / V1) ×100
Or
%R = ((I2R02 cos Φ +/- I2X02 sin Φ) / V2) ×100
The above two equations are used based on the parameters are referred to primary or secondary sides. Hence, from the SC test data we can find out the regulation of a transformer. The positive sign is used for lagging power factor and negative sign is used for leading power factor.

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Losses In Transformers ; Hysteresis Loss, Eddy Current Loss,Efficiency

Hysteresis Eddy Current(Iron) or Core Losses and Copper Loss in Transformer

We have discussed about electrical transformer construction,working.When it comes to efficiency of the transformer it is above 95%.In modern power transformers we can get above 98% of efficiency.Electrical transformer is a static device,so no rotating losses or frictional,windage losses.So no mechanical losses occur in transformer.We consider only electrical losses in transformer.Now read efficiency of transformer and losses in transformer below.

Losses in Transformer

As we no machine in this world is ideal.Transformer is also not an exception for this.There are two types of losses in transformers they are
(i) Core Losses Or Iron Losses
(ii) Copper Loss In Transformer 

(i) Core Losses Or Iron Losses in Transformer

Eddy current,Hysteresis losses are considered as core losses of transformer.Core losses of transformer almost constant for a transformer after it is built for certain and frequency.Because eddy current loss and hysteresis loss depends on the magnetic properties,volume of the core which is used for the construction.As volume is fixed we can say core losses or iron losses strictly depends only on frequency.

Hysteresis Loss in transformer


Hysteresis losses occurs due to reversal of magnetization in the transformer core.The magnetizing and demonstration curve of any material will not be same.Some loss happens due to cohesive force between magnetic atoms. 
The hysteresis loss in transformer depends on the volume and grade of the iron, frequency of magnetic reversals and value of flux density. It can be given by, Steinmetz formula:
Wh= ηBmax1.6fV (watts)
where,   η = Steinmetz hysteresis constant
             V = volume of the core in m3

How to reduce Hysteresis Loss in Transformer?

We can reduce hysteresis losses by using Cold Rolled Grain Oriented (CRGO) Silicon Steel.In earlier days we used silicon steel as transformer core after that CRGO steel found as less hysteresis constant.

Eddy current loss in transformer

Transformer works only on alternating current,when AC current is supplied to the primary winding of transformer,it sets up alternating magnetizing flux. When this flux cuts the secondary winding,emf will induced in it.This main flux also cuts the core of the transformer,As we know whenever flux cuts the magnetic material emf will induce in it.which will result in small circulating currents in them due to closed path of the core. This induced current is called as eddy current. Due to eddy currents, some energy will be dissipated in the form of heat.

 We= ηB²f²T (watts)

W∝ T

where,   η = Steinmetz hysteresis constant
             T = Thickness of lamination in m

How to reduce Eddy current loss in transformer?

By making the core into laminations.In the above relation you can find that eddy current losses are directly proportional with square of it's thickness.As the lamination thickness is much smaller than the depth of penetration of the field, the eddy current loss can be reduced by reducing the thickness of the lamination. Present day we use lamination thickness of 0.25mm operated at 2 Tesla.By decreasing lamination thickness we can  reduce the eddy current losses in the core.This loss also remains constant until the frequency of operation is constant.

(ii) Copper Loss In Transformer 

Copper loss in transformer also known as ohmic losses.This loss due to resistance of copper winding.We know that when current flows through a conductor definitely there will be I²R loss in the form of heat.


1.Primary copper losses in transformer takes place due to the flow of current in the primary winding of transformer.


2.Secondary copper losses takes place due to the flow of current in the secondary winding of transformer.
                                  
Total copper losses=I²R=(I1)²R1+(I2)²R2

where,I1,I2 and R1,R2 are current and resistances of primary ,secondary winding respectively.

The primary and secondary resistances differ from their d.c. values due to skin effect and the temperature rise of the winding.

Apart from these major losses we have dielectric loss in transformer.As it's name says dielectric losses takes place in the insulation coating of the transformer due to the large electric stress.It is constant and in the case of low rating transformers it is neglected.

Efficiency Of Transformer

Like all machines efficiency of a transformer can be defined as the output power divided by the input power.

Efficiency = output / input 

As a transformer being highly efficient[95-99%], output and input are having nearly same value,So it is impractical to measure the efficiency of transformer by using output / input.A practical method to find efficiency of a transformer is using, efficiency = (input - losses) / input = 1 - (losses / input).

Condition For Maximum Efficiency

Let,
Copper loss = (I1)²R1
Iron loss = Wi
Hence, efficiency of a transformer will be maximum when copper loss and iron losses are equal.That is Copper loss = Iron loss.

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