Showing posts with label transformer. Show all posts
Showing posts with label transformer. Show all posts

Current Transformer

In the last article we discussed about the Voltage Transformer(VT). Here we will discuss about the Current Transformer (CT). As we know the voltage and current transformers are used in the electric substations to transform high magnitude voltage and current to low magnitude voltage and current suitable for metering and protection purposes. This article require some basic knowledge about the transformer. It is even better if you go through the previous article about voltage transformer.

In the last article we had written two fundamental relationships between the voltage and current of both sides of the ideal transformer. 

For the current transformer the second equation is the main focus, which is reproduced here for convenience.

 The ampere-turns of both sides of the transformer are equal. Otherwise this equation is also called as the conservation of ampere-turns. So for the ideal transformer,

Ip  Np =  I Ns 

The subscripts 'p' and 's' are used for primary and secondary sides of the transformer respectively. Where the symbol I is used for current and 'N' is for number of turns. From the above formula it is easy to guess that for a transformer as Np and Ns are known values which does not change, so the value of secondary current Is is proportional to the primary current Ip, which is desired for accurate measurement of primary current. This is only true for ideal transformer. In case of actual transformer the primary and secondary side currents are not proportional. (see the equivalent circuit of the transformer in last article)

In an actual transformer a small part of the primary current is used as exciting current of the transformer core. So Ip and Is are no more proportional. Hence in the design of the current transformer the main aim is that the excitation current of the current transformer should be low.

Burden And Error

As said above, error is introduced in the measurement of the secondary current. The error happens both in the magnitude and phase angle of the current. The Error in magnitude is said as Current Ratio Error and the error of phase angle is called as Phase Error. the Curret Ratio Error in percentage is given as:

Current Ratio Error = (Kn * Is - Ip ) * 100 / Ip

Here Ip and Is are the actual primary and secondary currents (rms). 

Where as Kn = Ipr / Isr

Ipr and Isr are the rated primary and secondary currents and Kn is the rated transformation ratio.

Similar to the voltage transformer the load on the secondary of the current transformer is called as burden. The burden is either expressed in volt-amperes (VA) or in Ohms. The burden of the CT is the  sum of the burdens due to all  the equipment connected to the CT plus the burden due to the connecting cables.

The CT secondary current is usually rated at 5 Amp or 1 Amp. The secondary current rating should be chosen judiciously according to the application. Suppose we choose a CT of secondary current 5A. If the equipment for connection to the secondary of this CT requires long cables then the burden due to this connecting cables may be a considerable proportion of the total burden.

Burden Due to Cable = IR

R is the total resistance of connecting cables. I is the secondary current of CT. From the above you can have a feel about the value of burden due to cable for both the cases of 5A and 1A secondary rating.

So for the cases where long connecting leads are required then smaller current rating of 1A should be chosen.

Accuracy of current transformer is defined by different standards . The table below is a part of the IEC standard. The full table may be obtained from their web site.

Current Transformer Accuracy Classes (As IEC 60044-1)
(Partial Table)

Accuracy Class
Percent Rated current
Current Ratio Error (%)
Phase Error (Minutes)
Precise Measurement
Precise Measurement
Precise Measurement
Precise Measurement

In the table if the secondary current phasor leads the primary current phasor then the phase difference is positive, so the phase error is positive otherwise the error is negative. If you have drawn the phasor diagram for a basic transformer so that the angle between Ip and Is is nearly 180 degrees, then before doing the comparison the secondary phasor should be reversed. (if the CT is an ideal one then the angle between the two phasors should be zero). The above accuracy class table is valid for the burden between 25% to 100% of rated burden.


From the constructional point of view the current transformer is broadly available in two types. These two are Ring Type and Wound Core type.

The Wound Primary type has the primary winding of one or more turns over the core of the CT. The Window or Ring type does not have a primary winding. Of course both the types have a secondary winding.  The ring or window type has an opening in the center. The primary side is the single conductor which can pass through the opening (see figure below). 

Another variant of ring type is available which is called as bar type. Here a conductor bar is already occupying the center of the core and so a part of the CT. The terminals of the bar are brought out to be connected in series with the power circuit of which the current to be measured(or for protection). One more variation of ring type CT is the split core type. A spring mechanism allows the core to split and the primary conductor is allowed to the center of the core. Then the core is closed. This type of CT is mainly used for current measurement of low voltage distribution maintenance work below 450 volts.

The ring and bar types are mainly used for medium and low voltage CT where as wound primary type is mainly used for high and extra high voltage application.

The HV current transformers are designed as live tank type or dead tank type. The basic design of a CT for HV use is illustrated in figures below. The two types of CT mostly used in high voltage application are Hair Pin type and Top Core type. The Hair Pin type is so named as its primary side conductor resembles a hair pin.The Hair Pin type is mechanically more stable and robust in comparison to Top Core type. In HV application the core of the Hair Pin type is usually insulated by oil or SF6 (sulphur Hexa Fluoride) gas, which resides in a steel tank at the bottom position of the CT module.

The primary conductor in a Top Core type CT is straight passing through the core. The core is positioned at the top of the CT inside a box. See the above figures illustrating the relative position of different parts for both types of high voltage CT. Also in the figure below is shown a sketch of the Top Core type CT. It should be noted that for simplicity the secondary winding is shown as consisting of 2 or 3 turns concentrated at one place. But the actual CT whose secondary winding is comprised of several turns and the winding turns are evenly distributed along the core.

The CT is connected in series with the circuit of which the current is to be measured. When on the live system, the secondary side of the CT should never be left open. If the secondary is not used then the terminals of the secondary are shorted. If the secondary is left open then excessive high voltage is induced in the secondary which is harmful to the personnel and also to the equipment insulation. Also the CT should not be operated with a high resistance burden. The burden here is the total burden due to all the equipments connected to the CT plus the burden due to the cable.

The requirements of CT for the purpose of metering and protection are different. While for the metering purpose the accuracy within certain limits are very important where as in case of protection use, the CT should be able to give a reasonably proportionate secondary current for a variation of primary current which is many times the rated primary current.   The Accuracy Load Factor (A.L.F)  is the ratio of primary current upto which the CT gives reasonably proportionate secondary current  to the rated current. A.L.F is a number which gives the idea that upto how many times of the rated primary current, the CT gives reasonably proportionate secondary current. It is very essential for protection purposes, which is the requirement at faulted system condition with large fault current.

In this article and the previous article we have covered two very important equipment of a electric substation. Effort is made to present the information in simple and accurate ways. For the actual use of the CT and PT one should consult the manufacturer instruction sheet, guidelines and the relevant international and local standards. In the next article we will discuss little more and compare CT and PT and their connection.

Voltage Transformer

Voltage Transformer and current Transformer are known as Instrument Transformer. They are used in the substation to transform high magnitude voltage and current to low magnitude voltage and current suitable for metering and protection purposes.

While the main purpose of the instrument transformer is metering and protection it also isolate the high voltage side from the low voltage side comprised of  measurement and protection devices and circuits. Before proceeding further one should have some basic knowledge about working of the transformer. Here in this article we discuss about the voltage transformer (also called as potential transformer) and in the next article we will discuss about current transformer. The voltage transformers are broadly of two types. These are inductive VT and Capacitive VT (CVT). Let us first consider the inductive (electromagnetic) Voltave Transformer.

We Know the two fundamental laws of the inductive transformer.

For an ideal transformer,

V/ Np =  V/ Ns 

Ip  Np =  I Ns 

Subscripts 'p' and 's' are used for primary and secondary sides of the transformer. N is the number of turns of the respective side of the transformer.

The voltage and current transformers are used for measuring or protection purpose. Hence  in the ideal case we desire to get the value of secondary voltage which is proportionate to the primary voltage. The voltage transformer (potential transformer) is designed to closely follow the formula VNp =  VNs  for a specified range of operation. 

The equivalent circuit of an actual voltage transformer is shown in Fig-B.  Rand Lp are primary side resistance and leakage reactance of  transformer. Rand Ls are for the secondary of transformer. Rand Lm are the core loss component and magnetising reactance component respectively.  Error is mainly introduced in the measurement of voltage and phase angle due to these parameters of transformer.

 In comparison to current transformer the voltage transformers operate at a relatively higher point of the operating curve. In the design process care is taken to limit the exitation current otherwise the increased exciting current will result  in excessive voltage drop in the series impedances, so the error is increased. 

The inductive voltage transformer is constructed similar to power transformer. The secondary(low voltage) side winding has few turns wound over the magnetic core and the primary (high voltage) side winding is comprised of several turns wound over the primary winding.  The cross sectional area of the secondary side conductor is considerably more than the primary side conductor.  The secondary side voltage adopted is usually 100 volt or 110 volt.

A sketch of voltage transformer is shown in Fig-C. The porcelain insulator provide required creepage distance for HV terminal from ground. The tank made from galvanized steel filled with oil contains the magnetic core wound with primary and secondary windings of VT.  In a voltage transformer the core size is comparatively more so that a low flux is maintained at operating point.

Burden and Error

The instrument transformers are classified according to the allowed percentage error and burden. The load on the secondary side of the voltage transformer is called as burden(For instrument transformers burden terminology is used instead of load on the secondary side).The rated burden is specified in voltampere or VA. The Total burden of all the instruments connected to the secondary of the voltage transformer (VT) should be less than the rated burden. For example the VT secondary may be connected to a voltmeter, a watt meter, Integrating meter, a synchroscope and some relays. The sum of the burdens of all these equipments should be less than the rated burden of the VT. More over if the conductor lead used for connecting to these instruments is very long, then the  burden due to this long lead should also be added to the burdens of all the equipmets connected to the secondary of the Voltage Transformer. The burden of the VT can also be specified by impedance value in Ohm.

The voltage transformers has a specified rated transformation ratio. If kn is the rated transformation ratio then voltage error in percentage is given as,

Voltage Error = ( kn * Vs  Vp ) *100 /  V 

V and  Vp  are the actual primary and secondary voltage. 

And Kn is the ratio of rated primary voltage to rated secondary voltage.  

The  Accuracy class of voltage transformer (VT & CVT) is defined by the IEC. The table below display the limits specified  for the accuracy classes.

Voltage Transformer Accuracy Classes (As IEC 60044-2)

Accuracy Class
Voltage Error (%)
Phase Error (Minutes)
Precise Measurement

(Phase angle Error expressed in Minutes. One degree = 60 minutes)

The protection VTs are less accurate than the metering VTs. For revenue metering purposes the VT with accuracy class 0.2 may be preferred. For indicating meters less accuracy class like 1.0 may be chosen.

For the metering VTs the above accuracy of VT should be valid for voltage range between 80% to 120% of the rated voltage. For the protection VTs the above accuracy of VT should be valid for voltage range from 5% to  Vf times the rated voltage.  Vf  is the voltage factor. Vhas been defined by IEC. Vf is equal to 1.5 for solidly earthed system and 1.9 for the system which is not solidly earthed(See IEC standard).
For both metering and protection VTs, the above accuracy of VT should be valid for the burden between 25% to 100%. of rated burden.

Capacitor Voltage Transformer (CVT)

The above described inductive voltage transformer is usually economical for system voltage rating upto 132 kV. For higher system voltage at Extra High Voltage (EHV) and Ultra High Voltage(UHV), Capacitor Voltage Transformers (CVT) are used. At system voltage above 38 kV the inductive VT is not cost effective. The CVT is basically comprised of a capacitor voltage divider (see figure below) and an inductive Voltage transformer (as described above). The tapped voltage from the last unit of capacitor voltage divider is fed as input to the inductive VT. By using the capacitor voltage divider the system voltage is reduced to a voltage level suitable as input to the transformer.

As the circuit is capacitive a reactor L is connected in the primary so that the sum of the reactance L and the leakage reactance of the transformer compensate the capacitive effect at power frequency.

The phenomon of ferroresonance considerably influences the design of CVT. Under the conditions of various network disturbances or fault conditions the divider capacitor and inductor in the CVT form a series tuned resonating circuit. In resonance the magnetic circuit may saturate and overheat the transformer. It is necessary to damp out ferroresonance in CVT. So the CVTs are equipped with ferroresonance damping circuit as shown in the figure above.



Previously we already discussed basics of single phase transformer and three phase transformer. We also discussed about three phase transformer connections or Vector Groups. Now, here we will discuss about auto-transformers. Auto transformers have several applications. But first we will develop some basic concepts of autotransformer. Before proceeding further one should have some basic knowledge of transformer.

Auto transformers can be made in two ways. In one way it can be realized by additively connecting the primary and secondary windings of the two winding transformer. In other way the autotransformers can be thought of built as a single unit with one continuous winding. We will start from first approach and move to second.

Single Phase Autotransformer

Let us first consider a normal single phase two winding transformer. The schematic diagram of a  transformer is shown in Fig-A(i). We will obtain an autotransformer from this usual transformer.

Let the primary side and secondary side voltage ratings are respectively V1, I and V2, I respectively. Number of turns in primary and secondary side are N1 and Nrespectively. Now let us connect the transformers as shown in Fig-A(ii) with additive polarity. For the analysis purpose for better visibility we rearrange the windings in Fig-A(ii) as shown in Fig-B. Of course here we have shown a load connected across secondary

For the purpose of simplifying the analysis the transformer is considered as ideal. (In case of power transformer the ideal transformer analysis gives quite accurate result). The autotransformer analysis can be very simple if you recall two important concepts of a transformer.

  • The voltage developed in the windings are dependent on the flux linkages. The windings are wound on the same magnetic core so they link the same flux. Hence
                                                            V/ N1= V/ N2

             So whenever voltage V1 exist across primary winding, then voltage V2 will be induced across the
          secondary winding irrespective of changes in connections.
  •  Similarly the magnetic circuit demands that mmf should be balanced. It implies the primary side ampere turn should equal the secondary side ampere turn. Hence
                                                            I. N1= I. N2

It means current  I2 that flows  in secondary winding is associated with current  Iin primary winding according to above mmf balance formula.

In Fig-B the primary  of autotransformer is taken across both the windings where as secondary is across N2 winding.
The autotransformer is so loaded that the secondary current is I1+I2 . It makes the current flowing in the windings as I1 and I2   which are the rated values.
using KCL and KVL if the primary side voltage and current of the auto transformer is Vp and Ip and secondary side voltage and current of the auto transformer is Vs and Is then,

                                                            V= V1+V
                                                             Ip = I
                                                            Vs = V
                                                             Is = I1+I2.

Now the capacity of the autotransformer is (V1+V2).I1 or (I1+I2).V2

Using the voltage ratio and mmf balance formula it is quite easy to show that the autotransformer capacity formula can be simplified as

                  The capacity of autotransformer = Sa = (V+ V2).I= (I+ I2).V2 = V1 I1 (1 + N/ N1)
                                                                                          = V2 I2 (1 + N/ N1)   

                       Where as the capacity of our original transformer = S =V1 I1 = V2 I2

                                                                          So,   Sa = S(1 + N/ N1)

But (1 + N2 /N1) is always greater than 1.
Hence by forming an autotransformer the capacity of the resulting autotransformer is always more than the original isolated winding type transformer. In the so formed autotransformer it should be remembered that the voltage and current through the windings remains as before i.e the rated values. From the above formula it is clear that larger value of N2/N1  gives larger capacity of the autotransformer. 

In this case the voltage ratio of autotransformer =  (V1+V2)/ V2= V1 / V +1 = (N1 / N) + 1

                                                                Hence   V/ Vs =  (N1 / N) +1 =   (N1 / N) +1

From this formula it is clear that if  N2 /N1 is made large to increase the capacity then the voltage ratio between primary and secondary of autotransformer approaches 1. For this reason auto transformers are advantageous for use in power network when the voltage ratio between both sides is near unity. It is used in grid substations as interconnecting transformers (ICT). The autotransformers are used to interconnect two  different voltage levels. For example interconnection of 400kV and 220kV, 735kV and 345kV and 765kV and 400kV etc.. The voltage ratio should be less than 3:1 for more advantageous use.

Again look at the formula,
                                                     I. N1= I. N2

As we said  N2 /N1 should be large for adavantageous use.

                                      To achieve it, N2  should be much greater than N1

                                      It implies that  I2   will be much less than I1

The current I2  flows in the common winding of the autotransformer. Hence the auto transformer can be designed with N2 number of turns made of conductor of smaller cross section area, so resulting in a big saving.The autotransformers are cheaper and lighter in comparison to two winding transformers.

Just looking at the sketch you may think that instead of connecting two windings in additive ways. Why should not it be made of single winding and one terminal brought out from the middle as per requirement. Yes this is true and the autotransformer can be thought of made of a single winding having a part of winding common to primary and secondary .

Sometimes this method is used to obtain a variable secondary voltage. This case it is so designed that the middle contact can smoothly slides over the coil. It is commonly used in the academic electrical laboratories. This is usually called as Variac(Fig-C) or Dimmerstat. There are some other terminologies adopted by different manufacturers.  In this design it is not possible to adopt conductors of two different cross sectional area as in case of ICT where turns ratio is fixed(due to fixed voltage ratio) between primary and secondary. 

Autotransformers are also used for voltage regulation in distribution networks, for starting of induction motors and as lighting dimmers. Autotransformers are also used in electric traction.

One main disadvantage about autotransformer is that the primary and secondary are electrically connected.  So the electrical disturbance i.e high voltage transients from one side can be easily transmitted to the other side.
The other disadvantage is that the impedance of the autotransformer is considerably low, so the short circuit current will be more. More over an open circuit in common winding results in full primary side voltage across the load which is harmful.

But in several cases the advantages outweigh the disadvantages.

Three Phase Autotransformer

First thing is that the theory of single phase autotransformer is the basis of three phase autotransformer. Three single phase autotransfor bank can be used for forming a three phase transformer or a single unit  three phase autotransformer can be built. The three phase autotransformers (see Fig-D) are connected in star-star(Wye-Wye). If the autotransformers are connected as Delta-Delta, then phase difference between primary and secondary exist which is not desired (See Vector Groups).  

In three phase Y-Y connected power autotransformers an additional delta connected winding is used to take care of zero sequence currents (for unbalanced systems), and third harmonic currents.

Although we discussed here is for one particular case still we revealed the general approach. If you wish to connect load across the other winding, then you can proceed in a similar way.

Moreover the above analysis is for step down case. You can easily analyze for step up case by interchanging the position of source and load. In this case the direction of I1+I2 is reversed so also the directions of Iand I2. It should be recalled again that the change of direction of current in series winding is associated with change of direction of current in common winding to satisfy  mmf balance.

Transformer Zig-Zag Connection

We have already discussed all the main configurations of transformer vector groups. In the table of groups we also included transformer zig-zag  connections. Now I will show you how that is achieved. The transformer primary or secondary can be connected in zig-zag . Zig-zag connection is sometimes desired as the disadvantages in star and delta connection can be overcome by the use of zig-zag connection of transformer. Here we discuss only the techniques of achieving some connection.

Transformer connection is a good place for confusion. Applying these few points that we adopted will help understand the connections better.

·   Coloring is done to boost the visualization.
·   Windings of same color are on the same limb of core. For example all the three red color windings     are on one limb of core.
·   The voltage developed across the windings of same color are in phase (zero phase displacement) so they are drawn parallel to each other.
·   The analysis is done here considering anti-clockwise ABC phase sequence.
·   In any limb of core, windings terminals marked with even subscript are of one polarity and odd subscript are of other polarity. So for windings A1A2, a1a2 and a3a4, the terminals A1, a1 and a3 are of one polarity and A2, a2 and a4 are of other polarity.

Let us first consider  delta-zigzag (Dz0) connection

Delta-zigzag (Dz0) connection

In zig zag transformer connection, there are three windings on each of the three limbs of the core, one for primary and two for secondary. Both the windings of secondary are of equal turns.

The windings A1A2, a1a2 and a3a4 are wound on the same limb of the core hence they are all colored ‘red’. Similarly the other windings.

Although looking at the diagram and applying IEC coding, you can easily verify the Dz0 connection, still you might find it difficult to draw. How can we obtain Dz0 connection?

The easy way is first draw the phasor diagram and then derive the windings connection required for getting the desired phasor diagram or vector group.

First question is what we need? Here for Dz0, the phase difference between primary and secondary is 0 degree. We have to connect the windings in such a way so that it will give zero degree phase displacement between the primary and secondary (or say the primary and secondary are in phase).

See the diagram how connections are done to achieve a zigzag connection in the secondary.

In the primary side A2, B2 and C2 are the terminals brought out at the transformer bushings. In the secondary side a4, b4 and c4 are the terminals brought out at the transformer bushings. Other terminals are internally connected.

Actually for realizing the connection in secondary side the following sequence will help you.

·    Connect the primary side in Delta as usual or as we did in last article.

·    Then draw Delta(primary) side phasors.

·    NA2 phasor corresponds to a phase voltage in primary side. N is the virtual neutral, which does not exist physically in delta side, but found geometrically from the diagram. For obtaining the Dz0 configuration, the secondary ‘z’ side phasor diagram should be such so that the corresponding phase voltage (na4 here) phasor should be parallel to NA2.  This zero phase displacement can be obtained by connecting the windings a3a4 with b2b1 (in other limb) in series. Clearly b1 should be connected to a3 and not the other ways.

·    The resultant phasor is the sum of the two phasors.
              na4 = b2b1 + a3a4
Voltage phasors b2b1 and B1B2 are out of phase (180 degree phase difference), so the arrow head direction. Above addition is the phasor addition and not the arithmetic one.

·    Similarly obtain the resultant phasors for other two phases by recognizing the symmetry.

This way we get the secondary neutral point 'n' by connecting a2, b2 and c2 together. Of course unlike the primary side neutral 'N',  here the secondary side neutral 'n' is real and brought out at the bushing.

So in this way we can realize the connection of windings from the phasor diagram. Accordingly the windings are connected. It is important that we realised the connection from the phasor diagram and rearranged the windings in Delta and Zigzag shape for better view.

Delta-Zigzag (Dz6) connection 

Here the primary side connection is same as previous case. In the secondary side we have just reversed the direction of phasors in previous case and automatically get Dz6 vector group. Of course now the phasors are rearranged to obey the rules of phasor addition.

For phase 'a', na3=b1b2+a4a3. Compare it with previous Dz0 case.

  • Now the phasors are reversed and b2 is required to be connected to a4 (in Dz0 case b1 is connected to a3
  • Terminal a3 not (a4) is brought out at the transformer bushing
  • Secondary side neutral 'n' is obtained by connecting a1, b1 and c1 together
Now the secondary side windings are connected as per the phasor diagram. See fig-B

Star-Zigzag (Yz1) connection

Below (fig-C) is the connection and phasor diagram of Yz1 notation. It is left for the reader to verify the vector group. The reader should also practice the connections for other vector groups and corresponding phasor diagrams.

Transformer Vector Groups

The three phase transformer windings can be connected several ways. Based on the windings' connection, the vector group of the transformer is determined.

The transformer vector group is indicated on the Name Plate of transformer by the manufacturer.
The vector group indicates the phase difference between the primary and secondary sides, introduced due to that particular configuration of transformer windings connection.

The Determination of vector group of transformers is very important before connecting two or more transformers in parallel. If two transformers of different vector groups are connected in parallel then phase difference exist between the secondaries of the transformers and large circulating current flows between the two transformers which is very detrimental.

The three phase transformer primary and secondary windings are mainly connected in the following ways
  • Wye - Wye (also called Star-Star)
  • Wye - Delta (also called Star-Delta)
  • Delta -Wye ( also called Delta-Star)
  • Delta - Delta
The Star connection is also called Wye as it resembles the English letter 'Y'. As both the names Star and Wye are equally used we have the freedom to use them interchangeably. Of course some people also use the term 'Mesh' in place of 'Delta'. Let us first consider the Wye - Delta type where three primary windings are  connected in Wye and the three secondary windings in Delta.

For this whole article you have to remember few points below to enhance learning. It is applicable for both single unit type and single-phase bank of transformer type.
  • The windings A1A2 and a1a2 are wound on the same limb of core. So also the other two sets of windings. (In case of 3-phase bank of transformers the two windings correspond to same single phase transformer). 
  • The primary and secondary  windings on the same limb of the core are shown with same color. 
  • The windings on Delta and Star sides are diagrammatically rearranged in Delta and Star like shapes(according to connection) respectively just to enhance learning.
  • The voltage developed in the windings shown with same color(placed on same limb of core) are in phase(or zero phase displacement). Hence the corresponding phasors are drawn parallel to each other.

Wye - Delta (Star-Delta) transformer

The windings in the primary are connected in Wye(Star) and the secondary windings are connected in Delta.

In the primary side the three windings are A1-A2, B1-B2 and C1-C2.
Similarly the three secondary windings are a1-a2, b1-b2 and c1-c2.

It should be noted that both the windings A1-A2 of primary and a1-a2  of secondary are wound on the same limb of core. The naming of the terminals has been done according to their polarity. Other wise you can imagine that when A2 is positive with respect to A1, then also a2 is positive with respect to a1. Think similarly for the other windings.

See carefully the diagram below. A2,B2,C2 and a2,b2,c2 are respectively the primary and Secondary side terminals taken out side of transformer.

In the primary side the three windings are connected in star. So we have shorted A1, B1 and C1. This is the primary side (star side) neutral 'N'. In the secondary side the three windings are connected in delta. Here windings a1-a2 and A1-A2 are wound on the same limb of the core, so the corresponding voltage waves are in phase. Hence we have drawn a1-a2 parallel to A1-A2. similarly windings b1-b2 is drawn parallel to B1-B2 and c1-c2 drawn parallel to C1-C2. To see the actual physical placing of the windings on the core limbs of transformer see my (archived) article Three PhaseTransformer Basics. There also you can find one example for a bank of three single phase transformers used as three phase transformer.

In the phasor diagrams we have drawn primary side voltage phasors A1A2, B1B2 and C1C2. As usual for three phase system, these are the phasors displaced 120 degree from each other.Similarly in the secondary side voltage phasors a1a2, b1b2 and c1c2 are drawn. Just observe that a1a2 is parallel to A1A2, b1b2 is parallel to B1B2 and c1c2 is parallel to C1C2. I repeat here, that, this is because a1a2 and A1 A2 are in phase (as they are wound on the same limb of core). Similarly b1b2 and B1B2 are in phase and also c1c2 and C1C2 are in phase.

In the delta side we have so arranged that the phasors form the Delta. In the winding connection diagram a2 is connected to b1 so in the phasor diagram a2 and b1 are joined. Similarly by joining other two phasors according to their winding connection, we will automatically get the above phasor diagram.

The neutral (star point) physically exist in the star side . In the delta side physically the neutral point does not exist so it cannot be brought out. The delta side neutral is the imaginary point 'n' (geometrically found) which is equidistant from a2, b2 and c2.

c2a2, a2b2 and b2c2 are the line voltages in secondary delta side. So na2, nb2 and nc2 are the phase voltages in secondary side.

Now compare the primary side vector diagram and secondary side vector diagram. From the diagram it is clear that as if the secondary side  phasor triad  has been rotated counterclockwise with respect to primary side. From the geometry it can be confirmed that this angle is 30 degree. As the phasors are rotating counterclockwise, so the secondary side phasor a2n (phase voltage) lead the primary side phasor A2N (phase voltage) by 30 degree.

The transformers are classified into different Vector Groups depending on this phase difference between the primary and secondary sides, obtained due to different connection philosophy.

IEC has devised the standard code for determination of transformer vector group.
According to IEC the code for vector group consist of 2 or more letters followed by one or two digits.

  • The first letter is Capital letter which may be Y, D or Z, which stands for High voltage side Star, Delta or interconnected Star windings respectively.
  • The second letter  is a small letter which may be y, d or z which stands for low voltage side Star, Delta or interconnected Star windings respectively.
  • The third is the digits which stands for the phase difference between the high voltage and low voltage sides.

From the above three points, the first two are quite straightforward. The third one follows the clock convention as described below.

         In this convention the  transformer high voltage side phase voltage (line to Neutral) represented by Minute hand is fixed at 12 O'clock position and the low voltage side phase voltage (line to neutral) is represented by the Hour hand which is free to move. Clearly when the minute hand is fixed at 12 position the hour hand can take only twelve numbers of discrete positions 1, 2, 3 ... upto 12 (think it  twice). The angle between any two consecutive numbers in a clock is 30 degrees (360/12). Hence the angle between hour and minute hands can only be multiples of 30 degrees. See the figure.

Note: Remember that in star and zig-zag connection the neutral point exist physically and in delta connection the neutral does not exist physically and called virtual. But the line to neutral voltage can always be calculated algebraically/geometrically.

Now back to our discussion of Star-Delta transformer. We have already shown that the low voltage secondary side phasor a2n leads the high voltage primary side phasor A2N by 30 degree. (remember that the comparison is between the phase voltages). According to the clock convention this specific case represent 11 O' clock. So the above transformer connection can be represented by the symbol Yd11(or YNd11). N or n may be used for a brought out neutral. Here we will keep the material simple and will not mention the neutral symbol.

Let us change the connection slightly to get the Yd1 vector group. See Fig-B, here the primary side is as before, but in the secondary side a1 is connected to b2 etc. (compare with previous diagram).

In the above diagram the individual phasors are still the same as in Yd11 case. Here we have only rearranged the phasors of delta side, only to satisfy the connection changes in the secondary side. Here the clock face indicate One O' clock. As a result we obtain the Yd1 vector symbol.

Let us consider another important connection, Primary in Delta and Secondary Star connected.

Delta-Wye (Delta-Star) connection

Here the primary windings are connected in Delta and the secondary windings are connected in Star or Wye. The naming convention is similar to the Wye-Delta transformer.
    In the figure-C see how the windings of primary and secondary sides are connected in Delta and Star respectively. Also see the corresponding phasors.  In the Delta side each winding is subjected to line voltage, but in Wye side each winding is subjected to phase voltage (V/1.73).

    As already told and shown, although the neutral is not physically available in Delta side, but neutral point 'n' can be found geometrically . The arrow NA2 is the phasor representing phase voltage of high voltage side (primary). In the Star side(low voltage side) arrow na2 is clearly the phasor representing the phase voltage of low voltage side.

    From the diagram applying school geometry it is clear that na2 phasor lags NA2 phasor by 30 degrees.

    Applying IEC coding:
    NA2 is minute hand fixed at 12 O' clock and na2 is hour hand at 1 O' clock (as the angle between the two is 30 degrees)

    So the transformer is identified with Dy1 symbol.

    Similarly just slightly modifying the connection above we can get Dy11 notation. Here we have rearranged the windings in the primary side for connection modification and convenience. See Fig-D.

    If you understand the above examples then identifying Star-Star and Delta-Delta vector group are very easy. One can reasonably say that the phase difference between the primary and secondary sides of both these cases is zero. The vector group symbols will be Yy0 and Dd0.

    Remember the connections can be two different ways. Consider the Wye-Wye connection. In Yy0 (zero phase displacement between primary and secondary) secondary side neutral is obtained by shorting the terminals a1, b1 & c1 and a2,b2 & c2 are brought out terminals. In  Yy6 (180 degree phase  displaced) the neutral is obtained by shorting a2,b2 & c2 and a1,b1&c1 are brought out terminals. See Fig-E and Fig-F.

    Transformer connections are categorised into four main groups as tabulated below

    Undoubtedly transformers belonging to the same group can be operated in parallel without any difficulty.
     It is impossible to run in parallel, transformers in Group1 and 2 with transformers in Group3 and 4.You consider any one from group 1 or 2 and any one from group 3 or 4 and see the phase difference, which inhibit their paralleling.

    Also transformers in group1 and group2 cannot be operated in parallel as there is 180 degree phase difference between the two secondary windings. This can only be rectified by changing internal connection.

    Similarly if group3 and group4 transformers will be connected in parallel then there will be 60 degrees phase difference between their secondary windings. But with transformer external connection modification the phase difference of secondaries can be made zero. So group3 and group4 transformers can be operated in parallel with some external modification.

    Three Phase Transformer Basics

    The last post was about  single phase transformer. The theory is quite easy to understand. It is time for the three phase transformer. The basic theory remain the same. The three phase transformer can be realized by properly connecting three numbers of single phase transformer or designed as a single unit. The three nos of single phase type requires more materials and costlier where as the single unit three phase transformer requires less materials and so cheaper. When a winding fault occurs in one unit of the three single phase type then only that particular unit is replaced by a similar unit, but a winding fault in three phase single unit type requires replacement of the complete transformer.  The three single phase type requires more space.

    The three single phase type transformer are mainly used for extra high tension bulk power transmission and at generating stations. In this case four single phase transformers are used. Three single phase units are connected to grid and the fourth one is kept ready. Many times this type of arrangement is also done in Hydro power stations or other hilly areas where transportation of large single three phase unit  is not convenient or road permit is not available. Where space availability at the switch yard is less, the single unit 3-phase type should be preferred. 

    We have already discussed about single phase type. In the diagram it is shown how three numbers of single phase units can be connected for D-Y arrangement (primary in delta and secondary in star or Y). Three single phase units also called bank of transformers.

    In the diagram the windings of the same phase are colored same for easy understanding. The Vector(phasor) diagram shown below is also colored. The arrows denote the voltage in a particular winding. The magnitude of  red, green and blue arrows are same, denoting the same magnitude of voltage in all the three windings. The directions are 120 degrees apart, means the voltage waves are 120 degrees phase displaced from each other . The direction of arrow for example is BA, which is due to the polarity (dot mark) of winding shown ( you can think that 'A' is positive with respect to 'B'). similarly AC and BC. A balanced three phase system will always form the sides of the equilateral triangle. It is simple to remember that as the winding connections form the delta or star so also their respective voltage phasors.

    The delta side has a three-phase balanced supply, so also the voltage induced in the windings of the star(Y) side.

    For example in the delta (primary) side the voltage across the green color winding is CB(from C to B). The basic theory(recall the single phase case) says that the voltage induced in the star (secondary) green color winding is Nb (from N to b).
    So in the phasor diagram we have shown both green and pointing in the same direction. Similarly it is easy to think about the other windings (color wise). BA has the same direction as Na and AC has the same direction as Nc.

    The important thing is that CB is the line voltage but Nb is the phase voltage Also BA and and AC are line voltages where as Na and Nc are phase voltages.

    Using geometry, the line voltage and phase voltage magnitude and phase angle can be calculated. The line voltage magnitude is calculated by multiplying phase voltage with square root of 3.

                               Vline = 1.73 x Vph

    From our phasor diagram it is clear that there is 30 degree phase difference between Na and NA. More accurately voltage phasor Na is 30 degrees ahead of phasor NA. That is why voltage phasor ba is also 30 degrees ahead of phasor BA. 

    In a three phase transformer, the voltage is not only stepped up or stepped down, but also a phase displacement occurs between the  primary and secondary sides. There are several other ways of connecting the primary and secondary side windings which is done as per the requirements of customer.

    The above theory is true for both types of transformers. As both primary and secondary side windings and connection are visible in above type, so we have chosen the above for our analysis. Next we describe in brief the single unit three phase type transformer and also some common transformer considerations.

    For more detail about vector group click this link

    Three Phase Transformer (single Unit)

    In the diagram below is shown a three phase transformer basic design.The transformer has three limbs. Each phase winding is wound around one of the limbs. Each limb has two windings the primary and secondary windings. On each limb, the low voltage winding is placed nearer to the steel core and the high voltage winding is placed over the low voltage winding. Insulation is placed between the low voltage and high voltage windings. Also the low voltage winding is insulated from the core. The reason of placing the low voltage winding nearer to the core is the requirement of less insulation.  See the diagram below. In the diagram 'Top View' it is clearly shown how the primary and secondary windings are wound on the same leg of the core for each phase.

     To reduce eddy current losses the core of a transformer is made of thin sheets of silicon steel stacked together. The sheets of silicon steels are insulated from each other. The core assembly is put inside the steel tank filled with oil. The oil of the transformer acts as insulator between the winding coils and steel tank. The oil of the transformer also helps in cooling the transformer(more to discuss later). The transformer oil also dampen the noise originating from the core assembly.

    A balanced electrical system analysis is done in per phase basis. The transformer per phase impedance is very important for this purpose. The manufacturers of transformer provide this per phase impedance along with other transformer parameters and test values. The transformer is designed for achieving a specified impedance value. For distribution transformer the impedance is around 4 ohm and for large power transformer it may be 15 ohm or more as specified by the customer.

    We will discuss more about transformer in future. In the next post I hope for a little change