One of the main reasons that we use alternating AC voltages and currents in our homes and workplace’s is that it can be easily generated at a convenient voltage, transformed into a much higher voltage and then distributed around the country using a national grid of pylons and cables over very long distances. The reason for transforming the voltage is that higher distribution voltages implies lower currents and therefore lower losses along the grid.
These high AC transmission voltages and currents are then reduced to a much lower, safer and usable voltage level were it can be used to supply electrical equipment in our homes and workplaces, and all this is possible thanks to the basic Voltage Transformer.
A Typical Voltage Transformer
The Voltage Transformer can be thought of as an electrical component rather than an electronic component. A transformer basically is very simple static (or stationary) electro-magnetic passive electrical device that works on the principle of Faraday’s law of induction by converting electrical energy from one value to another.
The transformer does this by linking together two or more electrical circuits using a common oscillating magnetic circuit which is produced by the transformer itself. A transformer operates on the principals of “electromagnetic induction”, in the form of Mutual Induction.
Mutual induction is the process by which a coil of wire magnetically induces a voltage into another coil located in close proximity to it. Then we can say that transformers work in the “magnetic domain”, and transformers get their name from the fact that they “transform” one voltage or current level into another.
Transformers are capable of either increasing or decreasing the voltage and current levels of their supply, without modifying its frequency, or the amount of Electrical Power being transferred from one winding to another via the magnetic circuit.
A single phase voltage transformer basically consists of two electrical coils of wire, one called the “Primary Winding” and another called the “Secondary Winding”. For this tutorial we will define the “primary” side of the transformer as the side that usually takes power, and the “secondary” as the side that usually delivers power. In a single-phase voltage transformer the primary is usually the side with the higher voltage.
These two coils are not in electrical contact with each other but are instead wrapped together around a common closed magnetic iron circuit called the “core”. This soft iron core is not solid but made up of individual laminations connected together to help reduce the core’s losses.
The two coil windings are electrically isolated from each other but are magnetically linked through the common core allowing electrical power to be transferred from one coil to the other. When an electric current passed through the primary winding, a magnetic field is developed which induces a voltage into the secondary winding as shown.
In other words, for a transformer there is no direct electrical connection between the two coil windings, thereby giving it the name also of an Isolation Transformer. Generally, the primary winding of a transformer is connected to the input voltage supply and converts or transforms the electrical power into a magnetic field. While the job of the secondary winding is to convert this alternating magnetic field into electrical power producing the required output voltage as shown.
Notice that the two coil windings are not electrically connected but are only linked magnetically. A single-phase transformer can operate to either increase or decrease the voltage applied to the primary winding. When a transformer is used to “increase” the voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer.
However, a third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding. In other words, its output is identical with respect to voltage, current and power transferred. This type of transformer is called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits.
The difference in voltage between the primary and the secondary windings is achieved by changing the number of coil turns in the primary winding ( NP ) compared to the number of coil turns on the secondary winding ( NS ).
As the transformer is a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. This ratio, called the ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). This turns ratio value dictates the operation of the transformer and the corresponding voltage available on the secondary winding.
It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3-to-1. Then we can see that if the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true.
A transformer is all about “ratios”, and the turns ratio of a given transformer will be the same as its voltage ratio. In other words for a transformer: “turns ratio = voltage ratio”. The actual number of turns of wire on any winding is generally not important, just the turns ratio and this relationship is given as:
Assuming an ideal transformer and the phase angles: ΦP ≡ ΦS
Note that the order of the numbers when expressing a transformers turns ratio value is very important as the turns ratio 3:1 expresses a very different transformer relationship and output voltage than one in which the turns ratio is given as: 1:3.
A voltage transformer has 1500 turns of wire on its primary coil and 500 turns of wire for its secondary coil. What will be the turns ratio (TR) of the transformer.
This ratio of 3:1 (3-to-1) simply means that there are three primary windings for every one secondary winding. As the ratio moves from a larger number on the left to a smaller number on the right, the primary voltage is therefore stepped down in value as shown.
If 240 volts rms is applied to the primary winding of the same transformer above, what will be the resulting secondary no load voltage.
Again confirming that the transformer is a “step-down transformer as the primary voltage is 240 volts and the corresponding secondary voltage is lower at 80 volts.
Then the main purpose of a transformer is to transform voltages at preset ratios and we can see that the primary winding has a set amount or number of windings (coils of wire) on it to suit the input voltage. If the secondary output voltage is to be the same value as the input voltage on the primary winding, then the same number of coil turns must be wound onto the secondary core as there are on the primary core giving an even turns ratio of 1:1 (1-to-1). In other words, one coil turn on the secondary to one coil turn on the primary.
If the output secondary voltage is to be greater or higher than the input voltage, (step-up transformer) then there must be more turns on the secondary giving a turns ratio of 1:N (1-to-N), where N represents the turns ratio number. Likewise, if it is required that the secondary voltage is to be lower or less than the primary, (step-down transformer) then the number of secondary windings must be less giving a turns ratio of N:1 (N-to-1).
We have seen that the number of coil turns on the secondary winding compared to the primary winding, the turns ratio, affects the amount of voltage available from the secondary coil. But if the two windings are electrically isolated from each other, how is this secondary voltage produced?
We have said previously that a transformer basically consists of two coils wound around a common soft iron core. When an alternating voltage ( VP ) is applied to the primary coil, current flows through the coil which in turn sets up a magnetic field around itself, called mutual inductance, by this current flow according to Faraday’s Law of electromagnetic induction. The strength of the magnetic field builds up as the current flow rises from zero to its maximum value which is given asdΦ/dt.
As the magnetic lines of force setup by this electromagnet expand outward from the coil the soft iron core forms a path for and concentrates the magnetic flux. This magnetic flux links the turns of both windings as it increases and decreases in opposite directions under the influence of the AC supply.
However, the strength of the magnetic field induced into the soft iron core depends upon the amount of current and the number of turns in the winding. When current is reduced, the magnetic field strength reduces.
When the magnetic lines of flux flow around the core, they pass through the turns of the secondary winding, causing a voltage to be induced into the secondary coil. The amount of voltage induced will be determined by: N.dΦ/dt (Faraday’s Law), where N is the number of coil turns. Also this induced voltage has the same frequency as the primary winding voltage.
Then we can see that the same voltage is induced in each coil turn of both windings because the same magnetic flux links the turns of both the windings together. As a result, the total induced voltage in each winding is directly proportional to the number of turns in that winding. However, the peak amplitude of the output voltage available on the secondary winding will be reduced if the magnetic losses of the core are high.
If we want the primary coil to produce a stronger magnetic field to overcome the cores magnetic losses, we can either send a larger current through the coil, or keep the same current flowing, and instead increase the number of coil turns ( NP ) of the winding. The product of amperes times turns is called the “ampere-turns”, which determines the magnetising force of the coil.
So assuming we have a transformer with a single turn in the primary, and only one turn in the secondary. If one volt is applied to the one turn of the primary coil, assuming no losses, enough current must flow and enough magnetic flux generated to induce one volt in the single turn of the secondary. That is, each winding supports the same number of volts per turn.
As the magnetic flux varies sinusoidally, Φ = Φmax sinωt, then the basic relationship between induced emf, ( E ) in a coil winding of N turns is given by:
This is known as the Transformer EMF Equation. For the primary winding emf, N will be the number of primary turns, ( NP ) and for the secondary winding emf, N will be the number of secondary turns, ( NS ).
Also please note that as transformers require an alternating magnetic flux to operate correctly, transformers cannot therefore be used to transform or supply DC voltages or currents, since the magnetic field must be changing to induce a voltage in the secondary winding. In other words,Transformers DO NOT Operate on DC Voltages, ONLY AC.
If a transformers primary winding was connected to a DC supply, the inductive reactance of the winding would be zero as DC has no frequency, so the effective impedance of the winding will therefore be very low and equal only to the resistance of the copper used. Thus the winding will draw a very high current from the DC supply causing it to overheat and eventually burn out, because as we know I = V/R.
A single phase transformer has 480 turns on the primary winding and 90 turns on the secondary winding. The maximum value of the magnetic flux density is 1.1T when 2200 volts, 50Hz is applied to the transformer primary winding. Calculate:
a). The maximum flux in the core.
b). The cross-sectional area of the core.
c). The secondary induced emf.
Transformers are rated in Volt-amperes, ( VA ), or in larger units of Kilo Volt-amperes, ( kVA ). In an ideal transformer (ignoring any losses), the power available in the secondary winding will be the same as the power in the primary winding, they are constant wattage devices and do not change the power only the voltage to current ratio. Thus, in an ideal transformer the Power Ratio is equal to one (unity) as the voltage, V multiplied by the current, I will remain constant.
That is the electric power at one voltage/current level on the primary is “transformed” into electric power, at the same frequency, to the same voltage/current level on the secondary side. Although the transformer can step-up (or step-down) voltage, it cannot step-up power. Thus, when a transformer steps-up a voltage, it steps-down the current and vice-versa, so that the output power is always at the same value as the input power. Then we can say that primary power equals secondary power, ( PP = PS ).
Where: ΦP is the primary phase angle and ΦS is the secondary phase angle.
Note that since power loss is proportional to the square of the current being transmitted, that is:I2R, increasing the voltage, let’s say doubling ( ×2 ) the voltage would decrease the current by the same amount, ( ÷2 ) while delivering the same amount of power to the load and therefore reducing losses by factor of 4. If the voltage was increased by a factor of 10, the current would decrease by the same factor reducing overall losses by factor of 100.
A transformer does not require any moving parts to transfer energy. This means that there are no friction or windage losses associated with other electrical machines. However, transformers do suffer from other types of losses called “copper losses” and “iron losses” but generally these are quite small.
Copper losses, also known as I2R loss is the electrical power which is lost in heat as a result of circulating the currents around the transformers copper windings, hence the name. Copper losses represents the greatest loss in the operation of a transformer. The actual watts of power lost can be determined (in each winding) by squaring the amperes and multiplying by the resistance in ohms of the winding (I2R).
Iron losses, also known as hysteresis is the lagging of the magnetic molecules within the core, in response to the alternating magnetic flux. This lagging (or out-of-phase) condition is due to the fact that it requires power to reverse magnetic molecules; they do not reverse until the flux has attained sufficient force to reverse them.
Their reversal results in friction, and friction produces heat in the core which is a form of power loss. Hysteresis within the transformer can be reduced by making the core from special steel alloys.
The intensity of power loss in a transformer determines its efficiency. The efficiency of a transformer is reflected in power (wattage) loss between the primary (input) and secondary (output) windings. Then the resulting efficiency of a transformer is equal to the ratio of the power output of the secondary winding, PS to the power input of the primary winding, PP and is therefore high.
An ideal transformer is 100% efficient because it delivers all the energy it receives. Real transformers on the other hand are not 100% efficient and at full load, the efficiency of a transformer is between 94% to 96% which is quiet good. For a transformer operating with a constant voltage and frequency with a very high capacity, the efficiency may be as high as 98%. The efficiency, η of a transformer is given as:
where: Input, Output and Losses are all expressed in units of power.
Generally when dealing with transformers, the primary watts are called “volt-amps”, VA to differentiate them from the secondary watts. Then the efficiency equation above can be modified to:
It is sometimes easier to remember the relationship between the transformers input, output and efficiency by using pictures. Here the three quantities of VA, W and η have been superimposed into a triangle giving power in watts at the top with volt-amps and efficiency at the bottom. This arrangement represents the actual position of each quantity in the efficiency formulas.
and transposing the above triangle quantities gives us the following combinations of the same equation:
Then, to find Watts (output) = VA x eff., or to find VA (input) = W/eff., or to find Efficiency, eff. =W/VA, etc.
Then to summarise, a Transformer changes the voltage level (or current level) on its input winding to another value on its output winding using a magnetic field. A transformer consists of two electrically isolated coils and operates on Faraday’s principal of “mutual induction”, in which an EMF is induced in the transformers secondary coil by the magnetic flux generated by the voltages and currents flowing in the primary coil winding.
Both the primary and secondary coil windings are wrapped around a common soft iron core made of individual laminations to reduce eddy current and power losses. The primary winding of the transformer is connected to the AC power source which must be sinusoidal in nature, while the secondary winding supplies power to the load.
We can represent the transformer in block diagram form as follows:
The ratio of the transformers primary and secondary windings with respect to each other produces either a step-up voltage transformer or a step-down voltage transformer with the ratio between the number of primary turns to the number of secondary turns being called the “turns ratio” or “transformer ratio”.
If this ratio is less than unity, n < 1 then NS is greater than NP and the transformer is classed as a step-up transformer. If this ratio is greater than unity, n > 1, that is NP is greater than NS, the transformer is classed as a step-down transformer. Note that single phase step-down transformer can also be used as a step-up transformer simply by reversing its connections and making the low voltage winding its primary, and vice versa.
If the turns ratio is equal to unity, n = 1 then both the primary and secondary have the same number of windings, therefore the voltages and currents are the same for both windings.
This type of transformer is classed as an isolation transformer as both the primary and secondary windings of the transformer have the same number of volts per turn. The efficiency of a transformer is the ratio of the power it delivers to the load to the power it absorbs from the supply. In an ideal transformer there are no losses so no loss of power then Pin = Pout.
In the next tutorial to do with Transformer Basics, we will look at the physical Construction of a Transformer and see the different magnetic core types and laminations used to support the primary and secondary windings.
In the previous tutorial we saw that an inductor generates an induced emf within itself as a result of the changing magnetic field around its own turns, and when this emf is induced in the same circuit in which the current is changing this effect is called Self-induction, ( L ).
However, when the emf is induced into an adjacent coil situated within the same magnetic field, the emf is said to be induced magnetically, inductively or by Mutual induction, symbol ( M ). Then when two or more coils are magnetically linked together by a common magnetic flux they are said to have the property of Mutual Inductance.
Mutual Inductance is the basic operating principal of the transformer, motors, generators and any other electrical component that interacts with another magnetic field. Then we can define mutual induction as the current flowing in one coil that induces an voltage in an adjacent coil.
But mutual inductance can also be a bad thing as “stray” or “leakage” inductance from a coil can interfere with the operation of another adjacent component by means of electromagnetic induction, so some form of electrical screening to a ground potential may be required.
The amount of Mutual Inductance that links one coil to another depends very much on the relative positioning of the two coils. If one coil is positioned next to the other coil so that their physical distance apart is small, then nearly nearly all of the magnetic flux generated by the first coil will interact with the coil turns of the second coil inducing a relatively large emf and therefore producing a large mutual inductance value.
Likewise, if the two coils are farther apart from each other or at different angles, the amount of induced magnetic flux from the first coil into the second will be weaker producing a much smaller induced emf and therefore a much smaller mutual inductance value. So the effect of mutual inductance is very much dependant upon the relative positions or spacing, ( S ) of the two coils and this is demonstrated below.
The Mutual Inductance that exists between the two coils can be greatly increased by positioning them on a common soft iron core or by increasing the number of turns of either coil as would be found in a transformer.
If the two coils are tightly wound one on top of the other over a common soft iron core unity coupling is said to exist between them as any losses due to the leakage of flux will be extremely small. Then assuming a perfect flux linkage between the two coils the mutual inductance that exists between them can be given as.
Here the current flowing in coil one, L1 sets up a magnetic field around itself with some of these magnetic field lines passing through coil two, L2 giving us mutual inductance. Coil one has a current of I1 and N1 turns while, coil two has N2 turns. Therefore, the mutual inductance, M12 of coil two that exists with respect to coil one depends on their position with respect to each other and is given as:
Likewise, the flux linking coil one, L1 when a current flows around coil two, L2 is exactly the same as the flux linking coil two when the same current flows around coil one above, then the mutual inductance of coil one with respect of coil two is defined as M21. This mutual inductance is true irrespective of the size, number of turns, relative position or orientation of the two coils. Because of this, we can write the mutual inductance between the two coils as: M12 = M21 = M.
Hopefully we remember from our tutorials on Electromagnets that the self inductance of each individual coil is given as:
and
Then by cross-multiplying the two equations above, the mutual inductance that exists between the two coils can be expressed in terms of the self inductance of each coil.
giving us a final and more common expression for the mutual inductance between two coils as:
However, the above equation assumes zero flux leakage and 100% magnetic coupling between the two coils, L 1 and L 2. In reality there will always be some loss due to leakage and position, so the magnetic coupling between the two coils can never reach or exceed 100%, but can become very close to this value in some special inductive coils.
If some of the total magnetic flux links with the two coils, this amount of flux linkage can be defined as a fraction of the total possible flux linkage between the coils. This fractional value is called thecoefficient of coupling and is given the letter k.
Generally, the amount of inductive coupling that exists between the two coils is expressed as a fractional number between 0 and 1 instead of a percentage (%) value, where 0 indicates zero or no inductive coupling, and 1 indicating full or maximum inductive coupling.
In other words, if k = 1 the two coils are perfectly coupled, if k > 0.5 the two coils are said to be tightly coupled and if k < 0.5 the two coils are said to be loosely coupled. Then the equation above which assumes a perfect coupling can be modified to take into account this coefficient of coupling,k and is given as:
or
When the coefficient of coupling, k is equal to 1, (unity) such that all the lines of flux of one coil cuts all of the turns of the other, the mutual inductance is equal to the geometric mean of the two individual inductances of the coils. So when the two inductances are equal and L 1 is equal to L 2, the mutual inductance that exists between the two coils can be defined as:
Two inductors whose self-inductances are given as 75mH and 55mH respectively, are positioned next to each other on a common magnetic core so that 75% of the lines of flux from the first coil are cutting the second coil. Calculate the total mutual inductance that exists between them.
In the next tutorial about Inductors, we look at connecting together Inductors in Series and the affect this combination has on the circuits mutual inductance, total inductance and their induced voltages.
Thus far we have looked at transformers which have one single primary winding and one single secondary winding. But the beauty of transformers is that they allow us to have more than just one winding in either the primary or secondary side. Transformers which have more than one winding are known commonly as Multiple Winding Transformers.
The principal of operation of a multiple winding transformer is no different from that of an ordinary transformer. Primary and secondary voltages, currents and turns ratios are all calculated the same, the difference this time is that we need to pay special attention to the voltage polarities of each coil winding, the dot convention marking the positive (or negative) polarity of the winding, when we connect them together.
Multiple winding transformers, also known as a multi-coil, or multi-winding transformer, contain more than one primary or more than one secondary coil, hence their name, on a common laminated core. They can be either a single-phase transformer or a three-phase transformer, (multi-winding, multi-phase transformer) the operation is the same.
Multiple Winding Transformers can also be used to provide either a step-up, a step-down, or a combination of both between the various windings. In fact a multiple winding transformers can have several secondary windings on the same core with each one providing a different voltage or current level output.
As transformers operate on the principal of mutual induction, each individual winding of a multiple winding transformer supports the same number of volts per turn, therefore the volt-ampere product in each winding is the same, that is NP/NS = VP/VS with any turns ratio between the individual coil windings being relative to the primary supply.
In electronic circuits, one transformer is often used to supply a variety of lower voltage levels for different components in the electronic circuitry. A typical application of multiple winding transformers is in power supplies and Triac Switching Converters. So a transformer may have a number of different secondary windings, each of which is electrically isolated from the others, just as it is electrically isolated from the primary. Then each of the secondary coils will produce a voltage that is proportional to its number of coil turns for example.
Above shows an example of a typical “multiple winding transformer” which has a number of different secondary windings supplying various voltage levels. The primary windings can be used individually or connected together to operate the transformer from a higher supply voltages.
The secondary windings can be connected together in various configurations producing a higher voltage or current supply. It must be noted that connecting together transformer windings is only possible if the two windings are electrically identical. That is their current and voltage ratings are the same.
There are a number or multiple winding transformers available which have two primary windings of identical voltage and current ratings and two secondary windings also with identical voltage and current ratings. These transformers are designed so that they can be used in a variety of applications with the windings connected together in either a series or parallel combinations for higher primary voltages or secondary currents. These types of multiple winding transformers are more commonly called Dual Voltage Transformers as shown.
Here the transformer has two primary windings and two secondary windings, four in total. The connections to the primary or secondary windings must be made correctly with dual voltage transformers. If connected improperly, it is possible to create a dead short that will usually destroy the transformer when it is energized.
We said previously that dual voltage transformers can be connected to operate from power supplies of different voltage levels, hence their name “dual voltage transformers”. Then for example, lets say that the primary winding could have a voltage rating of 240/120V on the primary and 12/24V on the secondary. To achieve this, each of the two primary windings is, therefore, rated at 120V, and each secondary winding is rated at 12V. The transformer must be connected so that each primary winding receives the proper voltage. Consider the circuit below.
Here in this example, the two 120V rated primary windings are connected together in series across a 240V supply as the two windings are identical, half the supply voltage, namely 120V, is dropped across each winding and the same primary current flows through both. The two secondary windings rated at 12V, 2.5A each are connected in series with the secondary terminal voltage being the sum of the two individual winding voltages giving 24 Volts.
As the two windings are connected in series, the same amount of current flows through each winding, then the secondary current is the same at 2.5 Amps. So for a series connected secondary, the output in our example above is rated at 24 Volts, 2.5 Amps. Consider the parallel connected transformer below.
Here we have kept the two primary windings the same but the two secondary windings are now connected in a parallel combination. As before, the two secondary windings are rated at 12V, 2.5A each, therefore the secondary terminal voltage will be the same at 12 Volts but the current adds. Then for a parallel connected secondary, the output in our example above is rated at 12 Volts, 5.0 Amps.
Of course different dual voltage transformers will produce different amounts of secondary voltage and current but the principal is the same. Secondary windings must be correctly connected together to produce the required voltage or current output.
Dot orientation is used on the windings to indicate the terminals that have the same phase relationship. For example connecting two secondary windings together in opposite dot-orientation will cause the two magnetic flux’s to cancel each other out resulting in zero output.
Another type of dual voltage transformer which has only one secondary winding that is “tapped” at its electrical center point is called the Center-tap Transformer.
A center-tap transformer is designed to provide two separate secondary voltages, VA and VB with a common connection. This type of transformer configuration produces a two-phase, 3-wire supply.
The secondary voltages are the same and proportional to the supply voltage, VP, therefore power in each winding is the same. The voltages produced across each of the secondary winding is determined by the turns ratio as shown.
Above shows a typical center-tap transformer. The tapping point is in the exact center of the secondary winding providing a common connection for two equal but opposite secondary voltages. With the center-tap grounded, the output VA will be positive in nature with respect to the ground, while the voltage at the other secondary, VB will be negative and opposite in nature, that is they are 180o electrical degrees out-of-phase with each other.
However, there is one disadvantage of using an ungrounded center tapped transformer and that is it can produce unbalanced voltages in the two secondary windings due to unsymmetrical currents flowing in the common third connection because of unbalanced loads.
We can also produce a center-tap transformer using the dual voltage transformer from above. By connecting the secondary windings in series, we can use the center link as the tap as shown. If the output from each secondary is V, the total output voltage for the secondary winding will be equal to2V as shown.
Multiple Winding Transformers have many uses in electrical and electronic circuits. They can be used to supply different secondary voltages to different loads. Have their windings connected together in series or parallel combinations to provide higher voltages or currents, or have their secondary windings connected together in series to produce a center tapped transformer.
In the next tutorial about Transformers we will look at how Autotransformers work and see that they have only one main primary winding and no separate secondary winding.
Unlike the previous voltage transformer which has two electrically isolated windings called: the primary and the secondary, an Autotransformer has only one single voltage winding which is common to both sides. This single winding is “tapped” at various points along its length to provide a percentage of the primary voltage supply across its secondary load. Then the autotransformer has the usual magnetic core but only has one winding, which is common to both the primary and secondary circuits.
Therefore in an autotransformer the primary and secondary windings are linked together both electrically and magnetically. The main advantage of this type of transformer design is that it can be made a lot cheaper for the same VA rating, but the biggest disadvantage of an autotransformer is that it does not have the primary/secondary winding isolation of a conventional double wound transformer.
The section of winding designated as the primary part of the winding is connected to the AC power source with the secondary being part of this primary winding. An autotransformer can also be used to step the supply voltage up or down by reversing the connections. If the primary is the total winding and is connected to a supply, and the secondary circuit is connected across only a portion of the winding, then the secondary voltage is “stepped-down” as shown.
When the primary current IP is flowing through the single winding in the direction of the arrow as shown, the secondary current, IS, flows in the opposite direction. Therefore, in the portion of the winding that generates the secondary voltage, VS the current flowing out of the winding is the difference of IP and IS.
The Autotransformer can also be constructed with more than one single tapping point. Auto-transformers can be used to provide different voltage points along its winding or increase its supply voltage with respect to its supply voltage VP as shown.
The standard method for marking an auto-transformer windings is to label it with capital (upper case) letters. So for example, A, B, Z etc to identify the supply end. Generally the common neutral connection is marked as N or n. For the secondary tapping’s, suffix numbers are used for all tapping points along the auto-transformers primary winding. These numbers generally start at number 1 and continue in ascending order for all tapping points as shown.
An autotransformer is used mainly for the adjustments of line voltages to either change its value or to keep it constant. If the voltage adjustment is by a small amount, either up or down, then the transformer ratio is small as VP and VS are nearly equal. Currents IPand IS are also nearly equal.
Therefore, the portion of the winding which carries the difference between the two currents can be made from a much smaller conductor size, since the currents are much smaller saving on the cost of an equivalent double wound transformer.
However, the regulation, leakage inductance and physical size (since there is no second winding) of an autotransformer for a given VA or KVA rating are less than for a double wound transformer.
Autotransformer’s are clearly much cheaper than conventional double wound transformers of the same VA rating. When deciding upon using an autotransformer it is usual to compare its cost with that of an equivalent double wound type.
This is done by comparing the amount of copper saved in the winding. If the ratio “n” is defined as the ratio of the lower voltage to the higher voltage, then it can be shown that the saving in copper is: n.100%. For example, the saving in copper for the two autotransformer’s would be:
An autotransformer is required to step-up a voltage from 220 volts to 250 volts. The total number of coil turns on the transformer main winding is 2000. Determine the position of the primary tapping point, the primary and secondary currents when the output is rated at 10KVA and the economy of copper saved.
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Then the primary current is 45.4 amperes, the secondary current drawn by the load is 40 amperes and 5.4 amperes flows through the common winding. The economy of copper is 88%.
The autotransformer has many uses and applications including the starting of induction motors, used to regulate the voltage of transmission lines, and can be used to transform voltages when the primary to secondary ratio is close to unity.
An autotransformer can also be made from conventional two-winding transformers by connecting the primary and secondary windings together in series and depending upon how the connection is made, the secondary voltage may add to, or subtract from, the primary voltage.
As well as having a fixed or tapped secondary that produces a voltage output at a specific level, there is another useful application of the auto transformer type of arrangement which can be used to produce a variable AC voltage from a fixed voltage AC supply. This type of Variable Autotransformer is generally used in laboratories and science labs in schools and colleges and is known more commonly as the Variac.
The construction of a variable autotransformer, or variac, is the same as for the fixed type. A single primary winding wrapped around a laminated magnetic core is used as in the auto transformer but instead of being fixed at some predetermined tapping point, the secondary voltage is tapped through a carbon brush.
This carbon brush is rotated or allowed to slide along an exposed section of the primary winding, making contact with it as it moves supplying the required voltage level.
Then a variable autotransformer contains a variable tap in the form of a carbon brush that slides up and down the primary winding which controls the secondary winding length and hence the secondary output voltage is fully variable from the primary supply voltage value to zero volts.
The variable autotransformer is usually designed with a significant number of primary windings to produce a secondary voltage which can be adjusted from a few volts to fractions of a volt per turn. This is achieved because the carbon brush or slider is always in contact with one or more turns of the primary winding. As the primary coil turns are evenly spaced along its length. Then the output voltage becomes proportional to the angular rotation.
We can see that the variac can adjust the voltage to the load smoothly from zero to the rated supply voltage. If the supply voltage was tapped at some point along the primary winding, then potentially the output secondary voltage could be higher than the actual supply voltage. Variable autotransformer’s can also be used for the dimming of lights and when used in this type of application, they are sometimes called “dimmerstats”.
Variac’s are also very useful in Electrical and Electronics workshops and labs as they can be used to provide a variable AC supply. But caution needs to be taken with suitable fuse protection to ensure that the higher supply voltage is not present at the secondary terminals under fault conditions.
The Autotransformer have many advantages over conventional double wound transformers. They are generally more efficient for the same VA rating, are smaller in size, and as they require less copper in their construction, their cost is less compared to double wound transformers of the same VA rating. Also, their core and copper losses, I2R are lower due to less resistance and leakage reactance giving a superior voltage regulation than the equivalent two winding transformer.
In the next tutorial about Transformers we will look at another design of transformer which does not have a conventional primary winding wound around its core. This type of transformer is commonly called a Current Transformer and is used to supply ammeters and other such electrical power indicators.
The Current Transformer ( C.T. ), is a type of “instrument transformer” that is designed to produce an alternating current in its secondary winding which is proportional to the current being measured in its primary.
Current transformers reduce high voltage currents to a much lower value and provide a convenient way of safely monitoring the actual electrical current flowing in an AC transmission line using a standard ammeter. The principal of operation of a current transformer is no different from that of an ordinary transformer.
Typical Current Transformer
Unlike the voltage or Power Transformer looked at previously, the current transformer consists of only one or very few turns as its primary winding. This primary winding can be of either a single flat turn, a coil of heavy duty wire wrapped around the core or just a conductor or bus bar placed through a central hole as shown.
Due to this type of arrangement, the current transformer is often referred too as a “series transformer” as the primary winding, which never has more than a very few turns, is in series with the current carrying conductor.
The secondary winding may have a large number of coil turns wound on a laminated core of low-loss magnetic material which has a large cross-sectional area so that the magnetic flux density is low using much smaller cross-sectional area wire, depending upon how much the current must be stepped down. This secondary winding is usually rated at a standard 1 Ampere or 5 Amperes.
There are three basic types of current transformers: “wound”, “toroidal” and “bar”.
Current transformers can reduce or “step-down” current levels from thousands of amperes down to a standard output of a known ratio to either 5 Amps or 1 Amp for normal operation. Thus, small and accurate instruments and control devices can be used with CT’s because they are insulated away from any high-voltage power lines. There are a variety of metering applications and uses for current transformers such as with Wattmeter’s, power factor meters, watt-hour meters, protective relays, or as trip coils in magnetic circuit breakers, or MCB’s.
Generally current transformers and ammeters are used together as a matched pair in which the design of the current transformer is such as to provide a maximum secondary current corresponding to a full-scale deflection on the ammeter. In most current transformers an approximate inverse turns ratio exists between the two currents in the primary and secondary windings. This is why calibration of the CT is generally for a specific type of ammeter.
For most current transformers the primary and secondary currents are expressed as a ratio such as 100/5. This means that when 100 Amps is flowing in the primary winding it will result in 5 Amps flowing in the secondary winding. By increasing the number of secondary windings, N2, the secondary current can be made much smaller than the current in the primary circuit being measured. In other words, as N2 increases, I2 goes down by a proportional amount.
We know from our tutorial on double wound voltage transformers that its turns ratio is equal to:
from which we get:
As the primary usually consists of one or two turns whilst the secondary can have several hundred turns, the ratio between the primary and secondary can be quite large. For example, assume that the current rating of the primary winding is 100A. The secondary winding has the standard rating of 5A. Then the ratio between the primary and the secondary currents is 100A-to-5A, or 20:1. In other words, the primary current is 20 times greater than the secondary current.
It should be noted however, that a current transformer rated as 100/5 is not the same as one rated as 20/1 or subdivisions of 100/5. This is because the ratio of 100/5 expresses the “input/output current rating” and not the actual ratio of the primary to the secondary currents. Also note that the number of turns and the current in the primary and secondary windings are related by an inverse proportion.
But relatively large changes in a current transformers turns ratio can be achieved by modifying the primary turns through the CT’s window where one primary turn is equal to one pass and more than one pass through the window results in the electrical ratio being modified.
So for example, a current transformer with a relationship of say, 300/5A can be converted to another of 150/5A or even 100/5A by passing the main primary conductor through its interior window two or three times as shown. This allows a higher value current transformer to provide the maximum output current for the ammeter when used on smaller primary current lines.
A bar-type current transformer which has 1 turn on its primary and 160 turns on its secondary is to be used with a standard range of ammeters that have an internal resistance of 0.2Ω’s. The ammeter is required to give a full scale deflection when the primary current is 800 Amps. Calculate the maximum secondary current and secondary voltage across the ammeter.
Secondary Current:
Voltage across Ammeter:
We can see above that since the secondary of the current transformer is connected across the ammeter, which has a very small resistance, the voltage drop across the secondary winding is only 1.0 volts at full primary current. If the ammeter is removed, the secondary winding becomes open-circuited and the transformer acts as a step-up transformer resulting in a very high voltage equal to the ratio of: Vp(Ns/Np) being developed across the secondary winding.
So for example, assume our current transformer from above is connected to a 480 volt three-phase power line. Therefore:
This 76.8kV is why a current transformer should never be left open-circuited or operated with no-load attached when the main primary current is flowing through it. If the ammeter is to be removed, a short-circuit should be placed across the secondary terminals first to eliminate the risk of shock.
This is because when the secondary is open-circuited the iron core of the autotransformer operates at a high degree of saturation, which produces an abnormally large secondary voltage, and in our simple example above, this was calculated at 76.8kV!. This high secondary voltage could damage the insulation or cause electric shock if the CT’s terminals are accidentally touched.
There are many specialized types of current transformers now available. A popular and portable type which can be used to measure circuit loading are called “clamp meters” as shown.
Clamp meters open and close around a current carrying conductor and measure its current by determining the magnetic field around it, providing a quick measurement reading usually on a digital display without disconnecting or opening the circuit.
As well as the handheld clamp type CT, split core current transformers are available which has one end removable so that the load conductor or bus bar does not have to be disconnected to install it. These are available for measuring currents from 100 up to 5000 amps, with square window sizes from 1″ to over 12″ (25-to-300mm).
Then to summarise, the Current Transformer, (CT) is a type of instrument transformer used to convert a primary current into a secondary current through a magnetic medium. Its secondary winding then provides a much reduced current which can be used for detecting overcurrent, undercurrent, peak current, or average current conditions.
A current transformers primary coil is always connected in series with the main conductor giving rise to it also being referred to as a series transformer. The nominal secondary current is rated at 1A or 5A for ease of measurement. Construction can be one single primary turn as in Toroidal, Doughnut, or Bar types, or a few wound primary turns, usually for low current ratios.
Current transformers are intended to be used as proportional current devices. Therefore a current transformers secondary winding should never be operated into an open circuit, just as a voltage transformer should never be operated into a short circuit.
Very high voltages will result from open circuiting the secondary circuit of an energized CT so their terminals must be short-circuited if the ammeter is to be removed or when a CT is not in use before powering up the system.
In the next tutorial about Transformers we will look at what happens when we connect together three individual transformers in a star or delta configuration to produce a larger power transformer called a Three Phase Transformer used to supply 3-phase supplies.
Thus far we have looked at the construction and operation of the single-phase, two winding voltage transformer which can be used increase or decrease its secondary voltage with respect to the primary supply voltage. But voltage transformers can also be constructed for connection to not only one single phase, but for two-phases, three-phases, six-phases and even elaborate combinations up to 24-phases for some DC rectification transformers.
If we take three single-phase transformers and connect their primary windings to each other and their secondary windings to each other in a fixed configuration, we can use the transformers on a three-phase supply.
Three-phase, also written as 3-phase or 3φ supplies are used for electrical power generation, transmission, and distribution, as well as for all industrial uses. Three-phase supplies have many electrical advantages over Single-phase Power and when considering three-phase transformers we have to deal with three alternating voltages and currents differing in phase-time by 120 degrees as shown below.
A transformer can not act as a phase changing device and change single-phase into three-phase or three-phase into single phase. To make the transformer connections compatible with three-phase supplies we need to connect them together in a particular way to form a Three Phase Transformer Configuration.
A three phase transformer or 3φ transformer can be constructed either by connecting together three single-phase transformers, thereby forming a so-called three phase transformer bank, or by using one pre-assembled and balanced three phase transformer which consists of three pairs of single phase windings mounted onto one single laminated core.
The advantages of building a single three phase transformer is that for the same kVA rating it will be smaller, cheaper and lighter than three individual single phase transformers connected together because the copper and iron core are used more effectively. The methods of connecting the primary and secondary windings are the same, whether using just one Three Phase Transformeror three separate Single Phase Transformers. Consider the circuit below:
The primary and secondary windings of a transformer can be connected in different configuration as shown to meet practically any requirement. In the case of three phase transformer windings, three forms of connection are possible: “star” (wye), “delta” (mesh) and “interconnected-star” (zig-zag).
The combinations of the three windings may be with the primary delta-connected and the secondary star-connected, or star-delta, star-star or delta-delta, depending on the transformers use. When transformers are used to provide three or more phases they are generally referred to as a Polyphase Transformer.
But what do we mean by “star” and “delta” three-phase transformer connection. A three phase transformer has three sets of primary and secondary windings. Depending upon how these sets of windings are interconnected, determines whether the connection is a star or delta configuration. The available voltage which are each displaced from the other by 120 electrical degrees and flow of the transformers currents are also decided by the type of the electrical connection used on both the primary and secondary sides.
With three single-phase transformers connected together, the magnetic flux’s in the three transformers differ in phase by 120 time-degrees. With a single the three-phase transformer there are three magnetic flux’s in the core differing in time-phase by 120 degrees.
The standard method for marking three phase transformer windings is to label the three primary windings with capital (upper case) letters A, B and C, used to represent the three-phases of RED, YELLOW and BLUE. The secondary windings are labelled with small (lower case) letters a, b and c. Each winding has two ends normally labelled 1 and 2 so that, for example, the second winding of the primary has ends which will be labelled B1 and B2, while the third winding of the secondary will be labelled c1 and c2 as shown.
Symbols are generally used on a three phase transformer to indicate the type or types of connections used with upper case Y for star connected, D for delta connected and Z for interconnected star primary windings, with lower case y, d and z for their respective secondaries. Then, Star-Star would be labelled Yy, Delta-Delta would be labelled Dd and interconnected star to interconnected star would be Zz for the same types of connected transformers.
| Connection | Primary Winding | Secondary Winding |
| Delta | D | d |
| Star | Y | y |
| Interconnected | Z | z |
We now know that there are four ways in which three single-phase transformers may be connected together between primary and secondary three-phase circuits. The configurations are delta-delta, star-star, star-delta, and delta-star. Transformers for high voltage operation with the star connections has the advantage of reducing the voltage on an individual transformer, reducing the number of turns required and an increase in the size of the conductors, making the coil windings easier and cheaper to insulate than delta transformers.
The delta-delta connection nevertheless has one big advantage over the star-delta configuration, in that if one transformer of a group of three should become faulty or disabled, the two remaining ones will continue to deliver three-phase power with a capacity equal to approximately two thirds of the original output from the transformer unit.
In a delta connected ( Dd ) group of transformers, the line voltage, VL is equal to the supply voltage,VL = VS. But the current in each phase winding is given as: 1/√3 × IL of the line current, where IL is the line current.
One disadvantage of delta connected three phase transformers is that each transformer must be wound for the full-line voltage, (in our example above 100V) and for 57.7 per cent, line current. The greater number of turns in the winding, together with the insulation between turns, necessitate a larger and more expensive coil than the star connection. Another disadvantage with delta connected three phase transformers is that there is no “neutral” or common connection.
In the star-star arrangement ( Yy ), (wye-wye), each transformer has one terminal connected to a common junction, or neutral point with the three remaining ends of the primary windings connected to the three-phase mains supply. The number of turns in a transformer winding for star connection is 57.7 per cent, of that required for delta connection.
The star connection requires the use of three transformers, and if any one transformer becomes fault or disabled, the whole group might become disabled. Nevertheless, the star connected three phase transformer is especially convenient and economical in electrical power distributing systems, in that a fourth wire may be connected as a neutral point, ( n ) of the three star connected secondaries as shown.
.
The voltage between any line of the three-phase transformer is called the “line voltage”, VL, while the voltage between any line and the neutral point of a star connected transformer is called the “phase voltage”, VP. This phase voltage between the neutral point and any one of the line connections is 1/√3 × VL of the line voltage. Then above, the primary side phase voltage, VP is given as.
The secondary current in each phase of a star-connected group of transformers is the same as that for the line current of the supply, then IL = IS.
Then the relationship between line and phase voltages and currents in a three-phase system can be summarised as:
| Connection | Phase Voltage | Line Voltage | Phase Current | Line Current |
| Star |
VP = VL ÷ √3
|
VL = √3 × VP
|
IP = IL
|
IL = IP
|
| Delta |
VP = VL
|
VL = VP
|
IP = IL ÷ √3
|
IL = √3 × IP
|
Other possible connections for three phase transformers are star-delta Yd, where the primary winding is star-connected and the secondary is delta-connected or delta-star Dy with a delta-connected primary and a star-connected secondary.
Delta-star connected transformers are widely used in low power distribution with the primary windings providing a three-wire balanced load to the utility company while the secondary windings provide the required 4th-wire neutral or earth connection.
When the primary and secondary have different types of winding connections, star or delta, the overall turns ratio of the transformer becomes more complicated. If a three-phase transformer is connected as delta-delta ( Dd ) or star-star ( Yy ) then the transformer could potentially have a 1:1 turns ratio. That is the input and output voltages for the windings are the same.
However, if the 3-phase transformer is connected in star–delta, ( Yd ) each star-connected primary winding will receive the phase voltage,VP of the supply, which is equal to 1/√3 × VL.
Then each corresponding secondary winding will then have this same voltage induced in it, and since these windings are delta-connected, the voltage 1/√3 × VL will become the secondary line voltage. Then with a 1:1 turns ratio, a star–delta connected transformer will provide a √3:1 step-down line-voltage ratio.
Then for a star–delta ( Yd ) connected transformer the turns ratio becomes:
Likewise, for a delta–star ( Dy ) connected transformer, with a 1:1 turns ratio, the transformer will provide a 1:√3 step-up line-voltage ratio. Then for a delta-star connected transformer the turns ratio becomes:
Then for the four basic configurations of a three-phase transformer, we can list the transformers secondary voltages and currents with respect to the primary line voltage, VL and its primary line current IL as shown in the following table.
| Primary-Secondary Configuration |
Line Voltage | Line Current |
| Delta – Delta |
 |
 |
| Delta – Star |
 |
 |
| Star – Delta |
 |
 |
| Star – Star |
|
|
Where: n equals the transformers “turns ratio” (T.R.) of the number of secondary windings NS, divided by the number of primary windings NP. ( NS/NP )
So for example, the primary winding of a delta-star ( Dy ) connected 50VA transformer is supplied with a 100 volt, 50Hz three-phase supply. If the transformer has 500 turns on the primary and 100 turns on the secondary winding, calculate the secondary voltages and currents.
Given Data: transformer rating, 50VA, supply voltage, 100v, primary turns 500, secondary turns,100.
We have said previously that the three-phase transformer is effectively three interconnected single phase transformers on a single laminated core and considerable savings in cost, size and weight can be achieved by combining the three windings onto a single magnetic circuit as shown.
A three-phase transformer generally has the three magnetic circuits that are interlaced to give a uniform distribution of the dielectric flux between the high and low voltage windings. The exception to this rule is a three-phase shell type transformer. In the shell type of construction, even though the three cores are together, they are non-interlaced.
The three-limb core-type three-phase transformer is the most common method of three-phase transformer construction allowing the phases to be magnetically linked. Flux of each limb uses the other two limbs for its return path with the three magnetic flux’s in the core generated by the line voltages differing in time-phase by 120 degrees. Thus the flux in the core remains nearly sinusoidal, producing a sinusoidal secondary supply voltage.
The shell-type five-limb type three-phase transformer construction is heavier and more expensive to build than the core-type. Five-limb cores are generally used for very large power transformers as they can be made with reduced height. A shell-type transformers core materials, electrical windings, steel enclosure and cooling are much the same as for the larger single-phase types.
The construction of a simple two-winding transformer consists of each winding being wound on a separate limb or core of the soft iron form which provides the necessary magnetic circuit. This magnetic circuit, know more commonly as the “transformer core” is designed to provide a path for the magnetic field to flow around, which is necessary for induction of the voltage between the two windings.
However, this type of transformer construction were the two windings are wound on separate limbs is not very efficient since the primary and secondary windings are well separated from each other. This results in a low magnetic coupling between the two windings as well as large amounts of magnetic flux leakage from the transformer itself. But as well as this “O” shapes construction, there are different types of “transformer construction” and designs available which are used to overcome these inefficiencies producing a smaller more compact transformer.
The efficiency of a simple Transformer Construction can be improved by bringing the two windings within close contact with each other thereby improving the magnetic coupling. Increasing and concentrating the magnetic circuit around the coils may improve the magnetic coupling between the two windings, but it also has the effect of increasing the magnetic losses of the transformer core.
As well as providing a low reluctance path for the magnetic field, the core is designed to prevent circulating electric currents within the iron core itself. Circulating currents, called “eddy currents”, cause heating and energy losses within the core decreasing the transformers efficiency.
These losses are due mainly to voltages induced in the iron circuit, which is constantly being subjected to the alternating magnetic fields setup by the external sinusoidal supply voltage. One way to reduce these unwanted power losses is to construct the transformer core from thin steel laminations.
In all types of transformer construction, the central iron core is constructed from of a highly permeable material made from thin silicon steel laminations assembled together to provide the required magnetic path with the minimum of losses. The resistivity of the steel sheet itself is high reducing the eddy current losses by making the laminations very thin.
These steel transformer laminations vary in thickness’s from between 0.25mm to 0.5mm and as steel is a conductor, the laminations are electrically insulated from each other by a very thin coating of insulating varnish or by the use of an oxide layer on the surface.
Generally, the name associated with the construction of a transformer is dependant upon how the primary and secondary windings are wound around the central laminated steel core. The two most common and basic designs of transformer construction are the Closed-core Transformer and theShell-core Transformer.
In the “closed-core” type (core form) transformer, the primary and secondary windings are wound outside and surround the core ring. In the “shell type” (shell form) transformer, the primary and secondary windings pass inside the steel magnetic circuit (core) which forms a shell around the windings as shown below.
In both types of transformer core design, the magnetic flux linking the primary and secondary windings travels entirely within the core with no loss of magnetic flux through air. In the core type transformer construction, one half of each winding is wrapped around each leg (or limb) of the transformers magnetic circuit as shown above.
The coils are not arranged with the primary winding on one leg and the secondary on the other but instead half of the primary winding and half of the secondary winding are placed one over the other concentrically on each leg in order to increase magnetic coupling allowing practically all of the magnetic lines of force go through both the primary and secondary windings at the same time. However, with this type of transformer construction, a small percentage of the magnetic lines of force flow outside of the core, and this is called “leakage flux”.
Shell type transformer cores overcome this leakage flux as both the primary and secondary windings are wound on the same centre leg or limb which has twice the cross-sectional area of the two outer limbs. The advantage here is that the magnetic flux has two closed magnetic paths to flow around external to the coils on both left and right hand sides before returning back to the central coils.
This means that the magnetic flux circulating around the outer limbs of this type of transformer construction is equal to Φ/2. As the magnetic flux has a closed path around the coils, this has the advantage of decreasing core losses and increasing overall efficiency.
But you may be wondering as to how the primary and secondary windings are wound around these laminated iron or steel cores for this types of transformer constructions. The coils are firstly wound on a former which has a cylindrical, rectangular or oval type cross section to suit the construction of the laminated core. In both the shell and core type transformer constructions, in order to mount the coil windings, the individual laminations are stamped or punched out from larger steel sheets and formed into strips of thin steel resembling the letters “E’s”, “L’s”, “U’s” and “I’s” as shown below.
These lamination stampings when connected together form the required core shape. For example, two “E” stampings plus two end closing “I” stampings to give an E-I core forming one element of a standard shell-type transformer core. These individual laminations are tightly butted together during the transformers construction to reduce the reluctance of the air gap at the joints producing a highly saturated magnetic flux density.
Transformer core laminations are usually stacked alternately to each other to produce an overlapping joint with more lamination pairs being added to make up the correct core thickness. This alternate stacking of the laminations also gives the transformer the advantage of reduced flux leakage and iron losses. E-I core laminated transformer construction is mostly used in isolation transformers, step-up and step-down transformers as well as auto transformers.
Transformer windings form another important part of a transformer construction, because they are the main current-carrying conductors wound around the laminated sections of the core. In a single-phase two winding transformer, two windings would be present as shown. The one which is connected to the voltage source and creates the magnetic flux called the primary winding, and the second winding called the secondary in which a voltage is induced as a result of mutual induction.
If the secondary output voltage is less than that of the primary input voltage the transformer is known as a “Step-down Transformer”. If the secondary output voltage is greater then the primary input voltage it is called a “Step-up Transformer”.
Core-type Construction
The type of wire used as the main current carrying conductor in a transformer winding is either copper or aluminium. While aluminium wire is lighter and generally less expensive than copper wire, a larger cross sectional area of conductor must be used to carry the same amount of current as with copper so it is used mainly in larger power transformer applications.
Small kVA power and voltage transformers used in low voltage electrical and electronic circuits tend to use copper conductors as these have a higher mechanical strength and smaller conductor size than equivalent aluminium types. The downside is that when complete with their core, these transformers are much heavier.
Transformer windings and coils can be broadly classified in to concentric coils and sandwiched coils. In core-type transformer construction, the windings are usually arranged concentrically around the core limb as shown above with the higher voltage primary winding being wound over the lower voltage secondary winding.
Sandwiched or “pancake” coils consist of flat conductors wound in a spiral form and are so named due to the arrangement of conductors into discs. Alternate discs are made to spiral from outside towards the centre in an interleaved arrangement with individual coils being stacked together and separated by insulating materials such as paper of plastic sheet. Sandwich coils and windings are more common with shell type core construction.
Helical Windings also known as screw windings are another very common cylindrical coil arrangement used in low voltage high current transformer applications. The windings are made up of large cross sectional rectangular conductors wound on its side with the insulated strands wound in parallel continuously along the length of the cylinder, with suitable spacers inserted between adjacent turns or discs to minimize circulating currents between the parallel strands. The coil progresses outwards as a helix resembling that of a corkscrew.
Transformer Cores
The insulation used to prevent the conductors shorting together in a transformer is usually a thin layer of varnish or enamel in air cooled transformers. This thin varnish or enamel paint is painted onto the wire before it is wound around the core.
In larger power and distribution transformers the conductors are insulated from each other using oil impregnated paper or cloth. The whole core and windings is immersed and sealed in a protective tank containing transformer oil. The transformer oil acts as an insulator and also as a coolant.
We can not just simply take a laminated core and wrap one of the coil configurations around it. We could but we may find that the secondary voltage and current may be out-of-phase with that of the primary voltage and current. The two coil windings do have a distinct orientation of one with respect to the other. Either coil could be wound around the core clockwise or anticlockwise so to keep track of their relative orientations “dots” are used to identify a given end of each winding.
This method of identifying the orientation or direction of a transformers windings is called the “dot convention”. Then a transformers windings are wound so that the correct phase relations exist between the winding voltages with the transformers polarity being defined as the relative polarity of the secondary voltage with respect to the primary voltage as shown below.
The first transformer shows its two “dots” side by side on the two windings. The current leaving the secondary dot is “in-phase” with the current entering the primary side dot. Thus the polarities of the voltages at the dotted ends are also in-phase so when the voltage is positive at the dotted end of the primary coil, the voltage across the secondary coil is also positive at the dotted end.
The second transformer shows the two dots at opposite ends of the windings which means that the transformers primary and secondary coil windings are wound in opposite directions. The result of this is that the current leaving the secondary dot is 180o “out-of-phase” with the current entering the primary dot. So the polarities of the voltages at the dotted ends are also out-of-phase so when the voltage is positive at the dotted end of the primary coil, the voltage across the corresponding secondary coil will be negative.
Then the construction of a transformer can be such that the secondary voltage may be either “in-phase” or “out-of-phase” with respect to the primary voltage. In transformers which have a number of different secondary windings, each of which is electrically isolated from each other it is important to know the dot polarity of the secondary windings so that they can be connected together in series-aiding (secondary voltage is summed) or series-opposing (the secondary voltage is the difference) configurations.
The ability to adjust the turns ratio of a transformer is often desirable to compensate for the effects of variations in the primary supply voltage, the regulation of the transformer or varying load conditions. Voltage control of the transformer is generally performed by changing the turns ratio and therefore its voltage ratio whereby a part of the primary winding on the high voltage side is tapped out allowing for easy adjustment. The tapping is preferred on the high voltage side as the volts per turn are lower than the low voltage secondary side.
In this simple example, the primary tap changes are calculated for a supply voltage change of ±5%, but any value can be chosen. Some transformers may have two or more primary or two or more secondary windings for use in different applications providing different voltages from a single core.
The ability of iron or steel to carry magnetic flux is much greater than it is in air, and this ability to allow magnetic flux to flow is called permeability. Most transformer cores are constructed from low carbon steels which can have permeabilities in the order of 1500 compared with just 1.0 for air.
This means that a steel laminated core can carry a magnetic flux 1500 times better than that of air. However, when a magnetic flux flows in a transformers steel core, two types of losses occur in the steel. One termed “eddy current losses” and the other termed “hysteresis losses”.
Transformer Hysteresis Losses are caused because of the friction of the molecules against the flow of the magnetic lines of force required to magnetise the core, which are constantly changing in value and direction first in one direction and then the other due to the influence of the sinusoidal supply voltage.
This molecular friction causes heat to be developed which represents an energy loss to the transformer. Excessive heat loss can overtime shorten the life of the insulating materials used in the manufacture of the windings and structures. Therefore, cooling of a transformer is important.
Also, transformers are designed to operate at a particular supply frequency. Lowering the frequency of the supply will result in increased hysteresis and higher temperature in the iron core. So reducing the supply frequency from 60 Hertz to 50 Hertz will raise the amount of hysteresis present, decreased the VA capacity of the transformer.
Transformer Eddy Current Losses on the other hand are caused by the flow of circulating currents induced into the steel caused by the flow of the magnetic flux around the core. These circulating currents are generated because to the magnetic flux the core is acting like a single loop of wire. Since the iron core is a good conductor, the eddy currents induced by a solid iron core will be large.
Eddy currents do not contribute anything towards the usefulness of the transformer but instead they oppose the flow of the induced current by acting like a negative force generating resistive heating and power loss within the core.
Eddy current losses within a transformer core can not be eliminated completely, but they can be greatly reduced and controlled by reducing the thickness of the steel core. Instead of having one big solid iron core as the magnetic core material of the transformer or coil, the magnetic path is split up into many thin pressed steel shapes called “laminations”.
The laminations used in a transformer construction are very thin strips of insulated metal joined together to produce a solid but laminated core as we saw above. These laminations are insulated from each other by a coat of varnish or paper to increase the effective resistivity of the core thereby increasing the overall resistance to limit the flow of the eddy currents.
The result of all this insulation is that the unwanted induced eddy current power-loss in the core is greatly reduced, and it is for this reason why the magnetic iron circuit of every transformer and other electro-magnetic machines are all laminated. Using laminations in a transformer construction reduces eddy current losses.
The losses of energy, which appears as heat due both to hysteresis and to eddy currents in the magnetic path, is known commonly as “transformer core losses”. Since these losses occur in all magnetic materials as a result of alternating magnetic fields. Transformer core losses are always present in a transformer whenever the primary is energized, even if no load is connected to the secondary winding. Also these hysteresis and the eddy current losses are sometimes referred to as “transformer iron losses”, as the magnetic flux causing these losses is constant at all loads.
But there is also another type of energy loss associated with transformers called “copper losses”. Transformer Copper Losses are mainly due to the electrical resistance of the primary and secondary windings. Most transformer coils are made from copper wire which has resistance in Ohms, ( Ω ). This resistance opposes the magnetising currents flowing through them.
When a load is connected to the transformers secondary winding, large electrical currents flow in both the primary and the secondary windings, electrical energy and power ( or the I2 R ) losses occur as heat. Generally copper losses vary with the load current, being almost zero at no-load, and at a maximum at full-load when current flow is at maximum.
A transformers VA rating can be increased by better design and transformer construction to reduce these core and copper losses. Transformers with high voltage and current ratings require conductors of large cross-section to help minimise their copper losses. Increasing the rate of heat dissipation (better cooling) by forced air or oil, or by improving the transformers insulation so that it will withstand higher temperatures can also increase a transformers VA rating.
Then we can define an ideal transformer as having:
In the next tutorial about Transformers we will look at Transformer Loading of the secondary winding with respect to an electrical load and see the effect a “NO-load” and a “ON-load” connected transformer has on the primary winding current.
In the previous transformer tutorials, we have assumed that the transformer is ideal, that is one in which there are no core losses or copper losses in the transformers windings. However, in real world transformers there will always be losses associated with the transformers loading as the transformer is put “on-load”. But what do we mean by:Transformer Loading.
Well first let’s look at what happens to a transformer when it is in this “no-load” condition, that is with no electrical load connected to its secondary winding and therefore no secondary current flowing.
A transformer is said to be on “no-load” when its secondary side winding is open circuited, in other words, nothing is attached and the transformer loading is zero. When an AC Sinusoidal Supply is connected to the primary winding of a transformer, a small current, IOPEN will flow through the primary coil winding due to the presence of the primary supply voltage.
With the secondary circuit open, nothing connected, a back EMF along with the primary winding resistance acts to limit the flow of this primary current. Obviously, this no-load primary current ( Io ) must be sufficient to maintain enough magnetic field to produce the required back emf. Consider the circuit below.
The ammeter above will indicate a small current flowing through the primary winding even though the secondary circuit is open circuited. This no-load primary current is made up of the following two components:
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Note that this no-load primary current, Io is very small compared to the transformers normal full-load current. Also due to the iron losses present in the core as well as a small amount of copper losses in the primary winding, Io does not lag behind the supply voltage, Vp by exactly 90o, ( cosφ = 0 ), there will be some small phase angle difference.
A single phase transformer has an energy component, IE of 2 Amps and a magnetising component,IM of 5 Amps. Calculate the no-load current, Io and resulting power factor.
When an electrical load is connected to the secondary winding of a transformer and the transformer loading is therefore greater than zero, a current flows in the secondary winding and out to the load. This secondary current is due to the induced secondary voltage, set up by the magnetic flux created in the core from the primary current.
The secondary current, IS which is determined by the characteristics of the load, creates a self-induced secondary magnetic field, ΦS in the transformer core which flows in the exact opposite direction to the main primary field, ΦP. These two magnetic fields oppose each other resulting in a combined magnetic field of less magnetic strength than the single field produced by the primary winding alone when the secondary circuit was open circuited.
This combined magnetic field reduces the back EMF of the primary winding causing the primary current, IP to increase slightly. The primary current continues to increase until the cores magnetic field is back at its original strength, and for a transformer to operate correctly, a balanced condition must always exist between the primary and secondary magnetic fields. This results in the power to be balanced and the same on both the primary and secondary sides. Consider the circuit below.
We know that the turns ratio of a transformer states that the total induced voltage in each winding is proportional to the number of turns in that winding and also that the power output and power input of a transformer is equal to the volts times amperes, ( V x I ). Therefore:
But we also know previously that the voltage ratio of a transformer is equal to the turns ratio of a transformer as: “voltage ratio = turns ratio”. Then the relationship between the voltage, current and number of turns in a transformer can be linked together and is therefore given as:
Note that the current is inversely proportional to both the voltage and the number of turns. This means that with a transformer loading on the secondary winding, in order to maintain a balanced power level across the transformers windings, if the voltage is stepped up, the current must be stepped down and vice versa. In other words, “higher voltage — lower current” or “lower voltage — higher current”.
As a transformers ratio is the relationships between the number of turns in the primary and secondary, the voltage across each winding, and the current through the windings, we can rearrange the above transformer ratio equation to find the value of any unknown voltage, ( V ) current, ( I ) or number of turns, ( N ) as shown.
The total current drawn from the supply by the primary winding is the vector sum of the no-load current, Io and the additional supply current, I1 as a result of the secondary transformer loading and which lags behind the supply voltage by an angle of Φ. We can show this relationship as a phasor diagram.
If we are given currents, IS and Io, we can calculate the primary current, IP by the following methods.
A single phase transformer has 1000 turns on its primary winding and 200 turns on its secondary winding. The transformers “no-load” current taken from the supply is 3 Amps at a power factor of 0.2 lagging. Calculate the primary winding current, IP and its corresponding power factor, φ when the secondary current supplying a transformer loading is 280 Amperes at 0.8 lagging.
You may have noticed that the phase angle of the primary current, φP is very nearly the same as that of the secondary current phase angle, φS. This is due to the fact that the no-load current of 3 amperes is very small compared to the larger 56 amperes drawn by the primary winding from the supply.
Actual real life, transformer windings have impedances of both XL and R. These impedances need to be taken into account when drawing the phasor diagrams as these internal impedances cause voltage drops to occur within the transformers windings. The internal impedances are due to the resistance of the windings and an inductance drop called the leakage reactance resulting from the leakage flux. These internal impedances are given as:
So the primary and secondary windings of a transformer possess both resistance and reactance. Sometimes, it can be more convenient if all these impedances are on the same side of the transformer to make the calculations easier. It is possible to move the primary impedances to the secondary side or the secondary impedances to the primary side. The combined values of R and Limpedances are called “Referred Impedances” or “Referred Values”. The object here is to group together the impedances within the transformer and have just one value of R and XL in our calculations as shown.
In order to move a resistance from one side of the transformer to the other, we must first multiply them by the square of the turns ratio, ( Turns Ratio2 ) in our calculations. So for example, to move a resistance of 2Ω from one side to the other in a transformer that has a turns ratio of 8:1 will have a new resistive value of: 2 x 82 = 128Ω’s.
Note that if you move a resistance from a higher voltage side the new resistance value will increase and if you move the resistance from a lower voltage side its new value will decrease. This applies to the load resistance and reactance as well.
The Voltage Regulation of a Transformer is defined as the change in secondary terminal voltage when the transformer loading is at its maximum, i.e. full-load applied while the primary supply voltage is held constant. Regulation determines the voltage drop (or increase) that occurs inside the transformer as the load voltage becomes too low as a result of the transformers loading being to high which therefore affects its performance and efficiency.
Voltage regulation is expressed as a percentage (or per unit) of the no-load voltage. Then if Erepresents the no-load secondary voltage and V represents the full-load secondary voltage, the percentage regulation of a transformer is given as:
So for example, a transformer delivers 100 volts at no-load and the voltage drops to 95 volts at full load, the regulation would be 5%. The value of E – V will depend upon the internal impedance of the winding which includes its resistance, R and more significantly its AC reactance X, the current and the phase angle.
Also voltage regulation generally increases as the power factor of the load becomes more lagging (inductive). Voltage regulation with regards to the transformer loading can be either positive or negative in value, that is with the no-load voltage as reference, the change down in regulation as the load is applied, or with the full-load as reference and the change up in regulation as the load is reduced or removed.
In general, the regulation of the core type transformer when the transformer loading is high is not as good as the shell type transformer. This is because the shell type transformer has better flux distribution due to the interlacing of the coil windings.
In the next tutorial about Transformers we will look at the Multiple Winding Transformer which has more than one primary winding or more than one secondary winding and see how we can connect two or more secondary windings together in order to supply more voltage or more current to the connected load.
Electrical power transformer is a static device which
transforms electrical energy from one circuit to another without
any direct electrical connection and with the help of mutual
induction between two windings. It transforms power from one
circuit to another without changing its frequency but may be in
different voltage level.
This is a very short and simple definition of
transformer, as we will go through this portion of
tutorial related to electrical power transformer, we will
understand more clearly and deeply "what is transformer
?" and basictheory of transformer.
The working principle of transformer is very simple. It depends uponFaraday’s law of electromagnetic induction. Actually, mutual induction between two or more winding is responsible for transformation action in an electrical transformer.
According to these Faraday’s laws,
"Rate of change of flux linkage with respect to time is directly
proportional to the induced EMF in a conductor or coil".
Say you have one winding which is supplied by an alternating electrical source. The alternating current through the winding produces a continually changing flux or alternating flux that surrounds the winding. If any other winding is brought nearer to the previous one, obviously some portion of this flux will link with the second. As this flux is continually changing in its amplitude and direction, there must be a change in flux linkage in the second winding or coil. According to Faraday’s law of electromagnetic induction, there must be an EMF induced in the second. If the circuit of the later winding is closed, there must be an current flowing through it. This is the simplest form of electrical power transformer and this is the most basic of working principle of transformer.
For better understanding, we are trying to repeat the above explanation in a more brief way here. Whenever we apply alternating current to an electric coil, there will be an alternating flux surrounding that coil. Now if we bring another coil near the first one, there will be an alternating flux linkage with that second coil. As the flux is alternating, there will be obviously a rate of change in flux linkage with respect to time in the second coil. Naturally emf will be induced in it as per Faraday’s law of electromagnetic induction. This is the most basic concept of the theory of transformer.
The winding which takes electrical power from the
source, is generally known as primary winding of transformer. Here
in our above example it is first winding.
The winding which gives the desired output voltagedue
to mutual induction in the transformer, is commonly known
as secondary winding of transformer. Here in our example it is
second winding.
The above mentioned form of transformer is theoretically possible but not practically, because in open air very tiny portion of the flux of the first winding will link with second; so the current that flows through the closed circuit of later, will be so small in amount that it will be difficult to measure.
The rate of change of flux linkage depends upon the amount of linked flux with the second winding. So, it is desired to be linked to almost all flux of primary winding to the secondary winding. This is effectively and efficiently done by placing one low reluctance path common to both of the winding. This low reluctance path is core of transformer, through which maximum number of flux produced by the primary is passed through and linked with the secondary winding. This is the most basic theory of transformer.
The three main parts of a transformer are,
A transformer is a static machine used for transforming power from one circuit to another without changing frequency. This is a very basic definition of transformer.
The history of transformer was commenced in the year 1880. In the year 1950, 400KV electrical power transformer was introduced in high voltageelectrical power system. In the early 1970s, unit rating as large as 1100MVA was produced and 800KV and even higher KV class transformers were manufactured in year of 1980.
Generation of electrical power in
low voltage level is very much cost effective.
Hence electrical power is generated in
low voltage level. Theoretically, this
lowvoltage level power can be transmitted to the receiving
end. But if the voltagelevel of a power is increased,
the current of the power is reduced which causes
reduction in ohmic or I2R losses in the system,
reduction in cross sectional area of the conductor i.e. reduction
in capital cost of the system and it also improves the voltage
regulation of the system. Because of these, low level power
must be stepped up for efficient electrical power
transmission. This is done by step up transformer at the sending
side of the power system network. As this
high voltage power may not be distributed to the
consumers directly, this must be stepped down to the desired level
at the receiving end with the help of step down transformer. These
are the uses of electrical power
transformer in the electrical
power system.
Two winding transformers are generally used where ratio between
high voltage and lowvoltage is greater than 2. It is
cost effective to use auto transformer where the ratio
between high voltage and lowvoltage is less than 2.
Again three phase single unit transformer is more cost effective
than a bank of three single phase transformer unit in
a three phase system. But still it is preferable to use than
the later where power dealing is very large since such large size
of three phase single unitpower transformer may not be easily
transported from manufacturer’s place to work site.
Transformers can be categorized in different ways, depending upon their purpose, use, construction etc. The types of transformer are as follows,
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%.
Ideal transformer model is developed by considering a transformer which does not have any loss. That means the windings of the transformer are purely inductive and the core of transformer is loss free. There is zero leakage reactance of transformer. As we said, whenever we place a low reluctance core inside the windings, maximum amount of flux passes through this core, but still 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 transformer. In an ideal transformer, this leakage flux is also considered nil. That means, 100% flux passes through the core and links with both the primary and secondary windings of transformer. Although every winding is desired to be purely inductive but it has some resistance in it which causesvoltage drop and I2R loss in it. In such ideal transformer model, the windings are also considered ideal, that means resistance of the winding is zero.
Now if an alternating source voltage V1 is applied in the primary winding of that ideal transformer, there will be a counter self emf E1 induced in the primary winding which is purely 180° in phase opposition with supply voltage V1.
For developing counter emf E1 across the primary winding, it draws currentfrom the source to produce required magnetizing flux. As the primary winding is purely inductive, that current 90° lags from the supply voltage. This currentis called magnetizing current of transformer Iμ.
This alternating current Iμ produces an alternating magnetizing flux Φ which is proportional to that current and hence in phase with it. As this flux is also linked with secondary winding through the core of transformer, there will be another emf E2 induced in the secondary winding, this is mutually induced emf. As the secondary is placed on the same core where the primary winding is placed, the emf induced in the secondary winding of transformer, E2 is in the phase with primary emf E1 and in phase opposition with source voltage V1.
The above chapter was about a brief discussion about ideal transformer, it has also explained the basic ideal transformer model.
We have discussed about the theory of ideal transformer for better understanding of actual elementary theory of transformer. Now we will go through the practical aspects one by one of an electrical power transformerand try to draw vector diagram of transformer in every step. As we said that, in an ideal transformer; there are no core losses in transformer i.e. loss free core of transformer. But in practical transformer, there are hysteresis and eddy current losses in transformer core.
Let us consider one electrical transformer with only core losses, which means, it has only core losses but no copper loss and no leakage reactance of transformer. When an alternating source is applied in the primary, the source will supply the current for magnetizing the core of transformer. But this currentis not the actual magnetizing current, it is little bit greater than actual magnetizing current. Actually, total current supplied from the source has two components, one is magnetizing current which is merely utilized for magnetizing the core and other component of the source current is consumed for compensating the core losses in transformer. Because of this core loss component, the source current in transformer on no-load condition supplied from the source as source current is not exactly at 90° lags of supply voltage, but it lags behind an angle θ is less than 90°.
If total current supplied from source is Io, it will have one component in phase with supply voltage V1 and this component of the current Iw is core loss component. This component is taken in phase with source voltage, because it is associated with active or working losses in transformer. Other component of the source current is denoted as Iμ.
This component produces the alternating magnetic flux in the core, so it is watt-less; means it is reactive part of the transformer source current.
Hence Iμ will be in quadrature with V1 and in phase with alternating flux Φ.
Hence, total primary current in transformer on no-load condition can be represented as
Now you have seen how simple is to explain
the theory of
transformer in no-load.
Now we will examine the behavior of above
said transformer on load, that means load is
connected to the secondary terminals. Consider, transformer having
core loss but no copper loss and leakage reactance. Whenever load
is connected to the secondary winding, load current will start to
flow through the load as well as secondary winding. This load
current solely depends upon the characteristics of the load and
also upon secondary voltage of the transformer.
This current is called secondary current or
load current, here it is denoted as I2. As
I2 is flowing through the secondary, a self mmf
in secondary winding will be produced. Here it is
N2I2, where, N2 is the
number of turns of the secondary winding of transformer.
current in transformer on load”
title=”On-load Primary Current in Transformer”/>
This mmf or magneto motive force in the secondary winding produces flux φ2. This φ2 will oppose the main magnetizing flux and momentarily weakens the main flux and tries to reduce primary self induced emf E1. If E1 falls down below the primary source voltage V1, there will be an extracurrent flowing from source to primary winding. This extra primary current I2′ produces extra flux φ′ in the core which will neutralize the secondary counter flux φ2. Hence the main magnetizing flux of core, Φ remains unchanged irrespective of load.
So total current, this transformer draws from source can be divided into two components, first one is utilized for magnetizing the core and compensating the core loss i.e. Io. It is no-load component of the primary current. Second one is utilized for compensating the counter flux of the secondary winding. It is known as load component of the primary current.
Hence total no load primary current I1 of a electrical power transformer having no winding resistance and leakage reactance can be represented as follows
Where θ2 is the angle between
Secondary Voltage and Secondary Current of transformer.
Now we will proceed one further step toward more practical aspect of a transformer.
Now, consider the winding resistance of transformer
but no leakage reactance. So far we have discussed about the
transformer which has ideal windings, means winding with
no resistance and leakage reactance, but now we will
consider one transformer which has internal resistance in
the winding but no leakage reactance. As the windings are
resistive, there would be a voltagedrop in the windings.
We have proved earlier that, total primary currentfrom the source on load is I1. The voltage drop in the primary winding with resistance, R1 is R1I1. Obviously, induced emf across primary winding E1, is not exactly equal to source voltage V1. E1is less than V1 by voltage drop I1R1.
Again in the case of secondary,
the voltageinduced across the secondary winding,
E2 does not totally appear across
the load since it also drops by an amount
I2R2, where
R2 is the secondary
winding resistance and
I2 is
secondary current or load
current.
Similarly, voltage equation of the secondary side of the transformer will be
Now we will consider the condition, when there is leakage
reactance of transformer as well as winding resistance of
transformer.
Let leakage reactances of primary and secondary windings of the
transformer are X1 and
X2 respectively.
Hence total impedance of primary and secondary winding of transformer with resistance R1 and R2 respectively, can be represented as,
We have already established
the voltage equation of
a transformer on load, with
only resistances in the windings,
where voltage drops in the windings occur
only due to resistive voltage drop. But when
we consider leakage reactances of transformer
windings, voltage drop occurs in the winding
not only because of resistance, it is because
of impedance of transformerwindings. Hence,
actual voltage equation of a transformer can
easily be determined by just
replacing resistances
R1 &
R2 in the previously
establishedvoltage equations by
Z1 and
Z2.
Therefore, the voltage equations are,
Resistance drops are in the direction
of current vector but, reactive drop will be
perpendicular to the current vector as shown
in the above vector diagram of
transformer.
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.
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.
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 & 2. Suffix 1’s indicate similar polarity ends and so do 2’s.
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° – 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°-connection, of three phase 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°-connection.
But in LV side of transformer, if, a2 is connected to b1, b2 is connected to c1and 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°-connection, of three phase 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° 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 transformerconnection is
therefore known as − 30°-connection.
Star-delta + 30°-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 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.
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.
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.
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 highvoltage side electrical power transformer is about 10% cheaper than that of delta connected high voltage side transformer.
Let’s explain,
Let, the voltage ratio of transformer between HV & LV is K, voltage across HV winding is VH and voltage across LV winding is VL and voltage across transformer leads in HV side say Vp and in LV say Vs.
VH = Vp/√3 and
VL = Vs/√3
⇒ Vp / Vs =
VH / VL = K
⇒ VH = K. VL
Voltage difference between HV & LV winding,
VH = Vp/√3 and
VL = Vs
Voltage difference between HV & LV winding,
VH = Vp and
VL = Vs/√3
Voltage difference between HV & LV winding,
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–deltatransformer 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.