TRANSFORMER

TRANSFORMER

First i will tell you about what is the transformer?

• Transfrormer is a static device which is used to step up or step down the voltage at constant frequency.

                                    

                                                   figure of transformer.

First of all we have to know that why we are soo much interested to know about the transformers.

The answer is because of the transformer is the device which is frequently and mostly used in the electrical systems.The transformer is mostly used in the electrical system because of its higher efficiency.

We can use the step up transformers as a step down transformers also, so we can not called its windings as a primary and secondary instead of that we call it HIGH VOLTAGE WINDING and LOW VOLTAGE WINDINGS.
If the winding having less numbers of turns is connected to the supply side and the winding having large no. of turns are connected on the load side then the the transformer is step up transformers.
and when the winding having large no. of turns is connected to supply side and winding having less no of turns connected to load side then this transformer is called the step down transformer.

NOTE: We will never called the windings of the transformers as the primary windings and the secondary windings.
Windings having large no of turns is called high voltage winding and the winding having less no. of turns is called low voltage windings.

POWER TRANSFORMERS 
Power transformers are used in high power generations where large no. of electricity generation takes place.
We need the power transformers because when we transfer the supply from one place to other place (long distance transmissions) the losses occur in the low power to manipulate these losses we have to first step up these generated electricity to high level using the power transformers and then transmitted to the destination.

Types of transformer:

• STEP UP TRANSFORMER: Winding having large no. of turns are connected on the load side then the the transformer is step up transformers.
• STEP DOWN TRANSFORMER:Winding having less no of turns connected to load side then this transformer is called the step down transformers.

Parts of the transformer:
 These are the basic parts of a transformers are:

1. Laminated core : The core is used to support the windings in the transformer. It also provides a low reluctance path to the flow of magnetic flux. It is made of laminated soft iron core in order to reduce eddy current loss and Hysteresis loss. The composition of a transformer core depends on such factors as voltage, current, and frequency. The diameter of the transformer core is directly proportional to copper loss and is inversely proportional to iron loss. If the diameter of the core is decreased, the weight of the steel in the core is reduced, which leads to less core loss of the transformer and the copper loss increase. When the diameter of the core is increased, the opposite occurs.there are two types of cores are used CORE TYPE AND SHELL TYPE.
   
   
   
2. Windings: There are two windings wound over the transformer core that are insulated from each other. Windings consists of several turns of copper coils bundled together, and each bundle is connected in series to form a winding.
   Windings can be classified in two different ways:
   1. Based on the input and output supply
   2. Based on the voltage range
   Within the input/output supply classification, windings are further categorized:
   1. Primary windings - These are the windings to which the input voltage is applied.
   2. Secondary windings - These are the windings to which the output voltage is applied.
   Within the voltage range classification, windings are further categorized:
   1. High voltage winding - These are made of copper coil. The number of turns is the multiple of the number of turns in the low voltage windings. The copper coils are thinner than those of the low voltage windings.
   2. Low voltage windings - These have fewer turns than the high voltage windings. It is made of thick copper conductors. This is because the current in the low voltage windings is higher than that of high voltage windings.
   Transformers can be supplied from either low voltage (LV) or high voltage (HV) windings based on the requirement.
3. Insulating materials:Insulating paper and cardboard are used in transformers to isolate primary and secondary windings from each other and from the transformer core.
   Transformer oil is another insulating material. Transformer oil can actually have two functions: in addition to insulating it can also work to cool the core and coil assembly. The transformer's core and windings must be completely immersed in the oil. Normally, hydrocarbon mineral oils are used as transformer oil. Oil contamination is a serious problem because contamination robs the oil of its dielectric properties and renders it useless as an insulating medium.
4. Transformer oil:Transformer oil is used for cooling of the windings and also for the insulation.
5. Tap changer:The output voltage may vary according to the input voltage and the load. During loaded conditions, the voltage on the output terminal decreases, whereas during off-load conditions the output voltage increases. In order to balance the voltage variations, tap changers are used. Tap changers can be either on-load tap changers or off-load tap changers. In an on-load tap changer, the tapping can be changed without isolating the transformer from the supply. In an off-load tap changer, it is done after disconnecting the transformer. Automatic tap changers are also available.
6. Conservator:The conservator conserves the transformer oil. It is an airtight, metallic, cylindrical drum that is fitted above the transformer. The conservator tank is vented to the atmosphere at the top, and the normal oil level is approximately in the middle of the conservator to allow the oil to expand and contract as the temperature varies. The conservator is connected to the main tank inside the transformer, which is completely filled with transformer oil through a pipeline.
7. Breather:The breather controls the moisture level in the transformer. Moisture can arise when temperature variations cause expansion and contraction of the insulating oil, which then causes the pressure to change inside the conservator. Pressure changes are balanced by a flow of atmospheric air in and out of the conservator, which is how moisture can enter the system.
   If the insulating oil encounters moisture, it can affect the paper insulation or may even lead to internal faults. Therefore, it is necessary that the air entering the tank is moisture-free.
   The transformer's breather is a cylindrical container that is filled with silica gel. When the atmospheric air passes through the silica gel of the breather, the air's moisture is absorbed by the silica crystals. The breather acts like an air filter for the transformer and controls the moisture level inside a transformer. It is connected to the end of breather pipe.
8. Cooling tubes:Cooling tubes are used to cool the transformer oil. The transformer oil is circulated through the cooling tubes. The circulation of the oil may either be natural or forced. In natural circulation, when the temperature of the oil rises the hot oil naturally rises to the top and the cold oil sinks downward. Thus the oil naturally circulates through the tubes. In forced circulation, an external pump is used to circulate the oil.
9. Explosion vent:The explosion vent is used to expel boiling oil in the transformer during heavy internal faults in order to avoid the explosion of the transformer. During heavy faults, the oil rushes out of the vent. The level of the explosion vent is normally maintained above the level of the conservatory tank.

• NOTE: When DC voltage is connected across the transformer terminals the constant flux will be produced. The current through the windings increases rapidly, overheating and thereby damaging the windings.
• Transformer is rated in KVA only not in WATT it is because of the losses occurs in the transformer are due to the voltage and the current.
• A humming sound in comming from the transformer this is because of the core of the transformer is made of ferromagnetic material and ferromagnetic magnetic material has a property that when current is passes in a ferromagnetic material then there is some vibration occur in the material and because of this vibration in transformer the oil of the transformer also virate then a sound produces.

Emf Equation of Transformer

Emf equation of transformer can be established in a very easy way. Actually in electrical power transformer, one alternating electrical source is applied to the primary winding and due to this, magnetizing current flowing through the primary winding which produces alternating flux in the core of the transformer. This flux links with both primary and secondary windings. As this flux is alternating in nature, there must be a rate of change of flux. According to Faraday's law of electromagnetic inductions if any coil or conductor links with any changing flux, there must be an induced emf in it.

As the current source to primary is sinusoidal, the flux induced by it will be also sinusoidal. Hence, the function of flux may be considered as a sine function. Mathematically, derivative of that function will give a function for rate of change of flux linkage with respect to time. This later function will be a cosine function since d(sinθ)/dt = cosθ. So, if we derive the expression for rms value of this cosine wave and multiply it with number of turns of the winding, we will easily get the expression for rms value of induced emf of that winding. In this way, we can easily derive the emf equation of transformer.As the current source to primary is sinusoidal, the flux induced by it will be also sinusoidal. Hence, the function of flux may be considered as a sine function. Mathematically, derivative of that function will give a function for rate of change of flux linkage with respect to time. This later function will be a cosine function since d(sinθ)/dt = cosθ. So, if we derive the expression for rms value of this cosine wave and multiply it with number of turns of the winding, we will easily get the expression for rms value of induced emf of that winding. In this way, we can easily derive the emf equation of transformer.

Let's say, T is number of turns in a winding,

Φ_m is the maximum flux in the core in Wb. As per Faraday's  law of electromagnetic induction,Where φ is the instantaneous alternating flux and represented as,As the maximum value of cos2πft is 1, the maximum value of induced emf e is,To obtain the rms value of induced counter emf, divide this maximum value of e by √2.This is EMF equation of transformer.
If E₁ & E₂ are primary and secondary emfs and T₁ & T₂ are primary and secondary turns then, voltage ratio or turn ratio of the transformer is,

Transformation Ratio of Transformer

This constant is called transformation ratio of transformer , if T₂>T₁, K > 1, then the transformer is step up transformer. If T₂ < T₁, K < 1, then the transformer is step down transformer.

Voltage Ratio of Transformer

This above stated ratio is also known as voltage ratio of transformer if it is expressed as ratio of the primary and secondary voltages of transformer.

Turns Ratio of Transformer

As the voltage in primary and secondary of transformer is directly proportional to the number of turns in the respective winding, the transformation ratio of transformer is sometime expressed in ratio of turns and referred as turns ratio of transformer .

LEAKAGE FLUX: 

There is some flux which does not pass through the core but passes through the insulation used in the transformer.This flux does not take part in the transformation action of the transformer. This flux is called leakage flux of the transformer.

IDEAL TRANSFORMER

An ideal transformer is an imaginary transformer which does not have any loss in it, means no core losses, copper losses and any other losses in transformer. 

Efficiency of this transformer is considered as 100%.

Transformer which does not have any loss. That means the windings of the transformer are purely inductive and the core of the transformer is loss free. There is zero leakage flux of transformer As we said, whenever we place a low reluctance core inside the windings, maximum amount of flux passes through this core. 

In the ideal transformer we consider the zero winding resistance, leakage flux is nill, the total flux generated will get in secondary windings.

Parallel operation of transformer:

Why Parallel Operation of Transformers is required?

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

1. To maximize electrical power system efficiency:
   Generally electrical power transformer gives the maximum efficiency at full load. If we run numbers of transformers in parallel, we can switch on only those transformers which will give the total demand by running nearer to its full load rating for that time. When load increases, we can switch none by one other transformer connected in parallel to fulfill the total demand. In this way we can run the system with maximum efficiency.
2. To maximize electrical power system availability:
   If numbers of transformers run in parallel, we can shutdown any one of them for maintenance purpose. Other parallel transformers in system will serve the load without total interruption of power.
3. To maximize power system reliability:
   If any one of the transformers run in parallel, is tripped due to fault of other parallel transformers is the system will share the load, hence power supply may not be interrupted if the shared loads do not make other transformers over loaded.
4. To maximize electrical power system flexibility:
   There is always a chance of increasing or decreasing future demand of power system. If it is predicted that power demand will be increased in future, there must be a provision of connecting transformers in system in parallel to fulfill the extra demand because, it is not economical from business point of view to install a bigger rated single transformer by forecasting the increased future demand as it is unnecessary investment of money. Again if future demand is decreased, transformers running in parallel can be removed from system to balance the capital investment and its return.

Conditions for Parallel Operation of Transformers

When two or more transformers run in parallel, they must satisfy the following conditions for satisfactory performance. These are the conditions for parallel operation of transformers.
1. Same voltage ratio of transformer.
2. Same percentage impedance.
3. Same polarity.
4. Same phase sequence.

Same Voltage Ratio

If two transformers of different voltage ratio are connected in parallel with same primary supply voltage, there will be a difference in secondary voltages. Now say the secondary of these transformers are connected to same bus, there will be a circulating current between secondaries and therefore between primaries also. As the internal impedance of transformer is small, a small voltage difference may cause sufficiently high circulating current causing unnecessary extra I²R loss.

Same Percentage Impedance

The current shared by two transformers running in parallel should be proportional to their MVA ratings. Again, current carried by these transformers are inversely proportional to their internal impedance. From these two statements it can be said that, impedance of transformer running in parallel are inversely proportional to their MVA ratings. In other words, percentage impedance or per unit values of impedance should be identical for all the transformers that run in parallel.

Same Polarity

Polarity of all transformers that run in parallel, should be the same otherwise huge circulating current that flows in the transformer but no load will be fed from these transformers. Polarity of transformer means the instantaneous direction of induced emf in secondary. If the instantaneous directions of induced secondary emf in two transformers are opposite to each other when same input power is fed to both of the transformers, the transformers are said to be in opposite polarity. If the instantaneous directions of induced secondary emf in two transformers are same when same input power is fed to the both of the transformers, the transformers are said to be in same polarity.

Same Phase Sequence

The phase sequence or the order in which the phases reach their maximum positive voltage, must be identical for two parallel transformers. Otherwise, during the cycle, each pair of phases will be short circuited.
The above said conditions must be strictly followed for parallel operation of transformers but totally identical percentage impedance of two different transformers is difficult to achieve practically, that is why the transformers run in parallel may not have exactly same percentage impedance but the values would be as nearer as possible.

Auto Transformer

Auto transformer is a kind of electrical transformer where primary and secondary shares same common single winding. So basically it’s a one winding transformer.

Theory of Auto Transformer

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

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

If V₁ voltage is applied across the winding i.e. in between ′A′ and ′C′.

Hence, the voltage across the portion BC of the winding, will be,

As BC portion of the winding is considered as secondary, it can easily be understood that value of constant ′k′ is nothing but turn ratio or voltage ratio of that auto transformer.

When load is connected between secondary terminals i.e.between ′B′ and ′C′, load current I₂starts flowing. The current in the secondary winding or common winding is the difference of I₂ & I₁.

Copper Savings in Auto Transformer

Now we will discuss the savings of copper in auto transformer compared to conventional two winding transformer.

We know that weight of copper of any winding depends upon its length and cross-sectional area. Again length of conductor in winding is proportional to its number of turns and cross-sectional area varies with rated current.
So weight of copper in winding is directly proportional to product of number of turns and rated current of the winding.
Therefore, weight of copper in the section AC proportional to,

and similarly, weight of copper in the section BC proportional to,

Hence, total weight of copper in the winding of auto transformer proportional to,

In similar way it can be proved, the weight of copper in two winding transformer is proportional to,

N₁I₁ + N₂I₂

⇒ 2N₁I₁ (Since, in a transformer N₁I₁ = N₂I₂)

Let's assume, W_a and W_tw are weight of copper in auto transformer and two winding transformer respectively,

∴ Saving of copper in auto transformer compared to two winding transformer,

Auto transformer employs only single winding per phase as against two distinctly separate windings in a conventional transformer.

Advantages of using Auto Transformers

1. For transformation ratio = 2, the size of the auto transformer would be approximately 50% of the corresponding size of two winding transformer. For transformation ratio say 20 however the size would be 95 %. The saving in cost of the material is of course not in the same proportion. The saving of cost is appreciable when the ratio of transformer is low, that is lower than 2. Thus auto transformer is smaller in size and cheaper.
2. An auto transformer has higher efficiency than two winding transformer. This is because of less ohmic loss and core loss due to reduction of transformer material.
3. Auto transformer has better voltage regulation as voltage drop in resistance and reactance of the single winding is less.

Disadvantages of Using Auto Transformer

1. Because of electrical conductivit of the primary and secondary windings the lower voltage circuit is liable to be impressed upon by higher voltage. To avoid breakdown in the lower voltage circuit, it becomes necessary to design the low voltage circuit to withstand higher voltage.
2. The leakage flux between the primary and secondary windings is small and hence the impedance is low. This results into severer short circuit currents under fault conditions.
3. The connections on primary and secondary sides have necessarily needs to be same, except when using interconnected starring connections. This introduces complications due to changing primary and secondary phase angle particularly in the case of delta/delta connection.
4. Because of common neutral in a star/star connected auto transformer it is not possible to earth neutral of one side only. Both their sides should have their neutrality either earth or isolated.
5. It is more difficult to maintain the electromagnetic balance of the winding when voltage adjustment tappings are provided. It should be known that the provision of tapping on an auto transformer increases considerably the frame size of the transformer. If the range of tapping is very large, the advantages gained in initial cost is lost to a great event.

Applications of Auto Transformers

1. Compensating voltage drops by boosting supply voltage in distribution systems.
2. Auto transformers with a number of tapping are used for starting induction and synchronous motors.
3.  Auto transformer is used as variac in laboratory or where continuous variable over broad ranges are required.

 Instrument Transformer

Instrument transformers means current transformer and voltage transformer are used in electrical power system for stepping down currents and voltages of the system for metering and protection purpose. Actually relay and meters used for protection and metering, are not designed for high currents and voltages.
High currents or voltages of electrical power system can not be directly fed to relays and meters. CT steps down rated system current to 1 Amp or 5 Amp similarly voltage transformer step down system voltages to 110 V. The relays and meters are generally designed for 1 Amp, 5 Amp and 110 V.

Current Transformer or (CT)

A CT is an instrument transformer in which the secondary current is substantially proportional to primary current and differs in phase from it by ideally zero degree.

CT Accuracy Class or Current Transformer Class

A CT is similar to a electrical power transformer to some extent, but there are some difference in construction and operation principle. For metering and indication purpose, accuracy of ratio, between primary and secondary currents are essential within normal working range. Normally accuracy of current transformer required up to 125% of rated current; as because allowable system current must be below 125% of rated current. Rather it is desirable the CT core to be saturated after this limit since the unnecessary electrical stresses due to system over current can be prevented from the metering instrument connected to the secondary of the CT as secondary current does not go above a desired limit even primary current of the CT rises to a very high value than its ratings. So accuracy within working range is main criteria of a CT used for metering purpose. The degree of accuracy of a metering CT is expressed by CT accuracy class or simply current transformer class or CT class.

But in the case of protection, the CT may not have the accuracy level as good as metering CT although it is desired not to be saturated during high fault current passes through primary. So core of protection CT is so designed that it would not be saturated for long range of currents. If saturation of the core comes at lower level of primary current the proper reflection of primary current will not come to secondary, hence relays connected to the secondary may not function properly and protection system losses its reliability.

Suppose, you have one CT with current ratio 400/1 A and its protection core is situated at 500 A. If the primary current of the CT becomes 1000 A the secondary current will still be 1.25 A as because the secondary current will not increase after 1.25 A because of saturation. If actuating current of the relay connected the secondary circuit of the CT is 1.5 A, it will not be operated at all even fault level of the power circuit is 1000 A.
The degree of accuracy of a protection CT may not be as fine as metering CT but it is also expressed by CT accuracy class or simply current transformer class or CT class as in the case of metering current transformer but in little bit different manner.

THEORY

A CT functions with the same basic working principle of electrical power transformer, as we discussed earlier, but here is some difference. If a electrical power transformer or other general purpose transformer, primary current varies with load or secondary current. In case of CT, primary current is the system current and this primary current or system current transforms to the CT secondary, hence secondary current or burden current depends upon primary current of the current transformer.
Are you confused? OK let us clear you.
In a power transformer, if load is disconnected, there will be only magnetizing current flows in the primary. The primary of the power transformer takes current from the source proportional to the load connected with secondary. But in case of CT, the primary is connected in series with power line. So current through its primary is nothing but the current flows through that power line. The primary current of the CT, hence does not depend upon whether the load or burden is connected to the secondary or not or what is the impedance value of burden. Generally CT has very few turns in primary where as secondary turns is large in number. Say N_p is number of turns in CT primary and I_p is the current through primary. Hence, the primary AT is equal to N_pI_p AT.
If number of turns in secondary and secondary current in that current transformer are N_sand I_s respectively then Secondary AT is equal to N_sI_s AT.
In an ideal CT the primary AT is exactly is equal in magnitude to secondary AT.
So, from the above statement it is clear that if a CT has one turn in primary and 400 turns in secondary winding, if it has 400 A current in primary then it will have 1 A in secondary burden.
Thus the turn ratio of the CT is 400/1 A.

Error in Current Transformer or CT

But in an actual CT, errors with which we are connected can best be considered through a study of phasor diagram for a CT,I_s - Secondary current.
E_s - Secondary induced emf.
I_p - Primary current.
E_p - Primary induced emf.
K_T - Turns ratio = Numbers of secondary turns/number of primary turns.
I₀ - Excitation current.
I_m - Magnetizing component of I₀.
I_w - Core loss component of I₀.
Φ_m - Main flux.
Let us take flux as reference. EMF E_s and E_p lags behind the FLUX by 90°. The magnitude of the passers E_s and E_p are proportional to secondary and primary turns. The excitation current I_o which is made up of two components I_m and I_w.
The secondary current I₀ lags behind the secondary induced emf E_s by an angle Φ _s. The secondary current is now transferred to the primary side by reversing I_s and multiplied by the turns ratio K_T. The total current flows through the primary I_p is then vector sum of K_T I_sand I₀.

The Current Error or Ratio Error in Current Transformer or CT

From above passer diagram it is clear that primary current I_p is not exactly equal to the secondary current multiplied by turns ratio, i.e. K_TI_s. This difference is due to the primary current is contributed by the core excitation current. The error in current transformerintroduced due to this difference is called current error of CT or some times ratio error in current transformer.

Phase Error or Phase Angle Error in Current Transformer

For a ideal CT the angle between the primary and reversed secondary current vector is zero. But for an actual CT there is always a difference in phase between two due to the fact that primary current has to supply the component of the exiting current. The angle between the above two phases in termed as phase angle error in current transformer or CT.
Here in the pharos diagram it is β
the phase angle error is usually expressed in minutes.

Cause of Error in Current Transformer

The total primary current is not actually transformed in CT. One part of the primary current is consumed for core excitation and remaining is actually transformer with turns ratio of CT so there is error in current transformer means there are both ratio error in current transformer as well as a phase angle error in current transformer.

How to Reduce Error in Current Transformer

It is desirable to reduce these errors, for better performance. For achieving minimum error in current transformer, one can follow the following,

1. Using a core of high permeability and low hysteresis loss magnetic materials.
2. Keeping the rated burden to the nearer value of the actual burden.
3. Ensuring minimum length of flux path and increasing cross-sectional area of the core, minimizing joint of the core.
4. Lowering the secondary internal impedance.

Potential Transformer

Potential transformer or voltage transformer gets used in electrical power system for stepping down the system voltage to a safe value which can be fed to low ratings meters and relays. Commercially available relays and meters used for protection and metering, are designed for low voltage. This is a simplest form of potential transformer definition.

Voltage Transformer or Potential Transformer Theory

A voltage transformer theory or potential transformer theory is just like a theory of general purpose step down transformer. Primary of this transformer is connected across the phase and ground. Just like the transformer used for stepping down purpose, potential transformer i.e. PT has lower turns winding at its secondary.

The system voltage is applied across the terminals of primary winding of that transformer, and then proportionate secondary voltage appears across the secondary terminals of the PT.

The secondary voltage of the PT is generally 110 V. In an ideal potential transformer or voltage transformer, when rated burden gets connected across the secondary; the ratio of primary and secondary voltages of transformer is equal to the turns ratio and furthermore, the two terminal voltages are in precise phase opposite to each other. But in actual transformer, there must be an error in the voltage ratio as well as in the phase angle between primary and secondary voltages.
The errors in potential transformer or voltage transformer can be best explained by phasor diagram, and this is the main part of potential transformer theory.

Error in PT or Potential Transformer or VT or Voltage Transformer

I_s - Secondary current.
E_s - Secondary induced emf.
V_s - Secondary terminal voltage.
R_s - Secondary winding resistance.
X_s - Secondary winding reactance.
I_p - Primary current.
E_p - Primary induced emf.
V_p - Primary terminal voltage.
R_p - Primary winding resistance.
X_p - Primary winding reactance.
K_T - Turns ratio = Numbers of primary turns/number of secondary turns.
I₀ - Excitation current.
I_m - Magnetizing component of I₀.
I_w - Core loss component of I₀.
Φ_m - Main flux.
β - Phase angle error.
As in the case of current transformer and other purpose electrical power transformer, total primary current I_p is the vector sum of excitation current and the current equal to reversal of secondary current multiplied by the ratio 1/K_T.
If V_p is the system voltage applied to the primary of the PT, then voltage drops due to resistance and reactance of primary winding due to primary current I_p will come into picture. After subtracting this voltage drop from V_p, E_p will appear across the primary terminals. This E_p is equal to primary induced emf. This primary emf will transform to the secondary winding by mutual induction and transformed emf is E_s. Again this E_s will be dropped by secondary winding resistance and reactance, and resultant will actually appear across the burden terminals and it is denoted as V_s.
So, if system voltage is V_p, ideally V_p/K_T should be the secondary voltage of PT, but in reality; actual secondary voltage of PT is V_s.

Voltage Error or Ratio Error in Potential Transformer (PT) or Voltage Transformer (VT)

The difference between the ideal value V_p/K_T and actual value V_s is the voltage error or ratio error in a potential transformer, it can be expressed as,

Phase Error or Phase Angle Error in Potential or Voltage Transformer

The angle ′β′ between the primary system voltage V_p and the reversed secondary voltage vectors K_T.V_s is the phase error.

Cause of Error in Potential Transformer

The voltage applied to the primary of the potential transformer first drops due to the internal impedance of the primary. Then it appears across the primary winding and then transformed proportionally to its turns ratio, to the secondary winding. This transformed voltage across the secondary winding will again drop due to the internal impedance of the secondary, before appearing across burden terminals. This is the reason of errors in potential transformer.

Knee Point Voltage of Current Transformer PS Class

Current Transformer PS Class

Before understanding Knee Point Voltage of Current Transformer and current transformer PS class we should recall the terms instrument security factor of CT and accuracy limit factor.

Instrument Security Factor or ISF of Current Transformer

Instrument security factor is the ratio of instrument limit primary current to the rated primary current. Instrument limit current of a metering current transformer is the maximum value of primary current beyond which current transformer core becomes saturated. Instrument security factor of CT is the significant factor for choosing the metering instruments which to be connected to the secondary of the CT. Security or Safety of the measuring unit is better, if ISF is low. If we go through the example below it would be clear to us.

Suppose one current transformer has rating 100/1 A and ISF is 1.5 and another current transformer has same rating with ISF 2. That means, in first CT, the metering core would be saturated at 1.5 × 100 or 150 A, whereas is second CT, core will be saturated at 2 × 100 or 200 A. That means whatever may be the primary current of both CTs, secondary current will not increase further after 150 and 200 A of primary current of the CTs respectively. Hence maximum secondary current of the CTs would be 1.5 and 2.0 A.
As the maximum current can flow through the instrument connected to the first CT is 1.5 A which is less than the maximum value of current can flow through the instrument connected to the second CT i.e. 2 A. Hence security or safety of the instruments of first CT is better than later.
Another significance of ISF is during huge electrical fault, the short circuit current, flows through primary of the CT does not affect destructively, the measuring instrument attached to it as because, the secondary current of the CT will not rise above the value of rated secondary current multiplied by ISF.

Accuracy Limit Factor or ALF of Current Transformer

For protection current transformer, the ratio of accuracy limit primary current to the rated primary current. First we will explain, what is rated accuracy limit primary current?.

Broadly, this is the maximum value of primary current, beyond which core of the protection CT or simply protection core of of a CT starts saturated. The value of rated accuracy limit primary current is always many times more than the value of instrument limit primary current. Actually CT transforms the fault current of the electrical power system for operation of the protection relay connected to the secondary of that CT. If the core of the CT becomes saturated at lower value of primary current, as in the case of metering CT, the system fault will not reflect properly to the secondary, which may cause, the relays remain inoperative even the fault level of the system is large enough. That is why the core of the protection CT is made such a way that saturation level of that core must be high enough. But still there is a limit as because, it is impossible to make one magnetic core with infinitely high saturation level and secondly most important reason is that although the protection care should have high saturation level but that must be limited up to certain level otherwise total transformation of primary current during huge fault may badly damage the protection relays. So it is clear from above explanation, rated accuracy limit primary current, should not be so less, that it will not at all help the relays to be operated on the other hand this value must not be so high that it can damage the relays.

So, accuracy limit factor or ALF should not have the value nearer to unit and at the same time it should not be as high as 100. The standard values of ALF as per IS-2705 are 5, 10, 15, 20 and 30.

Knee Point Voltage of Current Transformer

This is the significance of saturation level of a CT core mainly used for protection purposes. The sinusoidal voltage of rated frequency applied to the secondary terminals of current transformer, with other winding being open circuited, which when increased by 10% cause the exiting current to increase 50%. The CT core is made of CRGO steel. It has its won saturation level. The EMF induced in the CT secondary windings is
E₂ = 4.44φfT₂ Where, f is the system frequency, φ is the maximum magnetic flux in Wb. T₂ is the number of turns of the secondary winding. The flux in the core, is produced by excitation current I_e. We have a non-liner relationship between excitation current and magnetizing flux. After certain value of excitation current, flux will not further increase so rapidly with increase in excitation current. This non-liner relation curve is also called B - H curve. Again from the equation above, it is found that, secondary voltage of acurrent transformer is directly proportional to flux φ. Hence one typical curve can be drawn from this relation between secondary voltage and excitation current as shown below.
It is clear from the curve that, linear relation between V and I_e is maintained from point A and K. The point ′A′ is known as ′ankle point′ and point ′K′ is known as ′Knee Point′.

In differential and restricted earth fault (REF) protection scheme, accuracy class and ALF of the CT may not ensure the reliability of the operation. It is desired that, differential and REF relays should not be operated when fault occurs outside the protected trasnformer. When any fault occurs outside the differential protection zone, the faulty current flows through the CTs of both sides of electrical power transformer. The both LV and HV CTs have magnetizing characteristics. Beyond the knee point, for slight increase in secondary emf a large increasing in excitation current is required. So after this knee point excitation current of both current transformers will be extremely high, which may cause mismatch between secondary current of LV & HV current transformers. This phenomena may cause unexpected tripping of power transformer. So the magnetizing characteristics of both LV & HV sides CTs, should be same that means they have same knee point voltage V_k as well as same excitation current I_eat V_k/2. It can be again said that, if both knee point voltage of current transformer and magnetizing characteristic of CTs of both sides of power transformer differ, there must be a mismatch in high excitation currents of the CTs during fault which ultimately causes the unbalancing between secondary current of both groups of CTs and transformer trips.

So for choosing CT for differential protection of transformer, one should consider current transformer PS class rather its convectional protection class. PS stands for protection special which is defined by knee point voltage of current transformer V_k and excitation current I_e at V_k/2.

Why CT Secondary Should Not Be Kept Open?

The electrical power system load current always flows through current transformer primary; irrespective of whether the current transformer is open circuited or connected to burden at its secondary.If CT secondary is open circuited, all the primary current will behave as excitation current, which ultimately produce huge voltage. Every current transformer has its won non-linear magnetizing curve, because of which secondary open circuit voltage should be limited by saturation of the core. If one can measure the rms voltage across the secondary terminals, he or she will get the value which may not appear to be dangerous. As the CT primary current is sinusoidal in nature, it zero 100 times per second.(As frequency of the current is 50 Hz). The rate of change of flux at every current zero is not limited by saturation and is high indeed. This develops extremely high peaks or pulses of voltage. This high peaks of voltage may not be measured by conventional voltmeter. But these high peaks of induced voltage may breakdown the CT insulation, and may case accident to personnel. The actual open-circuit voltage peak is difficult to measure accurately because of its very short peaks. That is why CT secondary should not be kept open.

Comparison between Single Three Phase and Bank of Three Single Phase Transformers for Three Phase System

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

Another advantage of using bank of three single phase transformers is that, if one unit of the bank becomes out of order, then the bank can be run as open delta.

Connection of Three Phase Transformer

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

Marking or Labeling the Different Terminals of Transformer

Terminals of each phase of HV side should be labeled as capital letters, A, B, C and those of LV side should be labeled as small letters a, b, c. Terminal polarities are indicated by suffixes 1 and 2. Suffix 1’s indicate similar polarity ends and so do 2’s.

Star-Star Transformer

Star-star transformer is formed in a 3 phase transformer by connecting one terminal of each phase of individual side, together. The common terminal is indicated by suffix 1 in the figure below. If terminal with suffix 1 in both primary and secondary are used as common terminal, voltages of primary and secondary are in same phase. That is why this connection is called zero degree connection or 0^o - connection.
If the terminals with suffix 1 is connected together in HV side as common point and the terminals with suffix 2 in LV side are connected together as common point, the voltages in primary and secondary will be in opposite phase. Hence, star-star transformer connection is called 180^o-connection, of three phase transformer.

Delta-Delta Transformer

In delta-delta transformer, 1 suffixed terminals of each phase primary winding will be connected with 2 suffixed terminal of next phase primary winding.If primary is HV side, then A₁ will be connected to B₂, B₁ will be connected to C₂ and C₁ will be connected to A₂. Similarly in LV side 1 suffixed terminals of each phase winding will be connected with 2 suffixed terminals of next phase winding. That means, a₁ will be connected to b₂, b₁ will be connected to c₂ and c₁ will be connected to a₂. If transformer leads are taken out from primary and secondary 2 suffixed terminals of the winding, then there will be no phase difference between similar line voltages in primary and secondary. This delta delta transformer connection is zero degree connection or 0^o-connection.

But in LV side of transformer, if, a₂ is connected to b₁, b₂ is connected to c₁ and c₂ is connected to a₁. The secondary leads of transformer are taken out from 2 suffixed terminals of LV windings, and then similar line voltages in primary and secondary will be in phase opposition. This connection is called 180^o-connection, of three phase transformer.

Star-Delta Transformer

Here in star-delta transformer, star connection in HV side is formed by connecting all the 1 suffixed terminals together as common point and transformer primary leads are taken out from 2 suffixed terminals of primary windings.The delta connection in LV side is formed by connecting 1 suffixed terminals of each phase LV winding with 2 suffixed terminal of next phase LV winding. More clearly, a₁ is connected to b₂, b₁ is connected to c₂ and c₁ is connected to a₂. The secondary (here it considered as LV) leads are taken out from 2 suffixed ends of the secondary windings of transformer. The transformer connection diagram is shown in the figure beside. It is seen from the figure that the sum of the voltages in delta side is zero. This is a must as otherwise closed delta would mean a short circuit. It is also observed from the phasor diagram that, phase to neutral voltage (equivalent star basis) on the delta side lags by − 30^o to the phase to neutral voltage on the star side; this is also the phase relationship between the respective line to line voltages. This star delta transformer connection is therefore known as − 30^o-connection. Star-delta + 30^o-connection is also possible by connecting secondary terminals in following sequence. a₂ is connected to b₁, b₂ is connected to c₁ and c₂ is connected to a₁. The secondary leads of transformer are taken out from 2 suffixed terminals of LV windings,

Delta-Star Transformer

Delta-star transformer connection of three phase transformer is similar to star – delta connection. If any one interchanges HV side and LV side of star-delta transformer in diagram, it simply becomes delta – star connected 3 phase transformer. That means all small letters of star-delta connection should be replaced by capital letters and all small letters by capital in delta-star transformer connection.

Delta-Zigzag Transformer

The winding of each phase on the star connected side is divided into two equal halves in delta zig zag transformer. Each leg of the core of transformer is wound by half winding from two different secondary phases in addition to its primary winding.

Star-Zigzag Transformer

The winding of each phase on the secondary star in a star-zigzag transformer is divided into two equal halves. Each leg of the core of transformer is wound by half winding from two different secondary phases in addition to its primary winding.

Choice Between Star Connection and Delta Connection of Three Phase Transformer

In star connection with earthed neutral, phase voltage i.e. phase to neutral voltage, is 1/√3 times of line voltage i.e. line to line voltage. But in the case of delta connection phase voltage is equal to line voltage. Star connected high voltage side electrical power transformeris about 10% cheaper than that of delta connected high voltage side transformer.

Let’s explain,
Let, the voltage ratio of transformer between HV and LV is K, voltage across HV winding is V_H and voltage across LV winding is V_L and voltage across transformer leads in HV side say V_p and in LV say V_s.

In Star-Star Transformer

Voltage difference between HV & LV winding,

In Star-Delta Transformer

Voltage difference between HV & LV winding,

In Delta-Star Transformer

Voltage difference between HV & LV winding,

For 132/33KV Transformer K = 4

Case 1
Voltage difference between HV & LV winding,Case 2
Voltage difference between HV & LV winding,Case 3
Voltage difference between HV & LV winding,In case 2 voltage difference between HV and LV winding is minimum therefore potential stresses between them is minimum, implies insulation cost in between these windings is also less. Hence for step down purpose star–delta transformer connection is most economical, design for transformer. Similarly it can be proved that for step up purpose delta-star three phase transformer connection is most economical.