Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase DAYANANDA SAGAR COLLEGE OF ENGINEERING (An Autonomous Institute affiliated to VTU, Approved by AICTE & ISO 9001:2008 Certified) (Accredited by National Assessment & Accreditation Council (NAAC) with ’A’ Grade) SHAVIGE MALLESWARA HILLS, KUMARASWAMY LAYOUT BENGALURU-560078

ELECTRICAL & ELECTRONICS ENGINEERING DEPARTMENT

Module-3- Three-phase Transformers

Three Phase Transformers

Three-phase Transformers are the backbone of electrical power distribution whether Delta or Star connected windings.

Thus far we have looked at the construction and operation of the single-phase, two winding voltage 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.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

Three Phase Voltages and Currents

Where: VL is the line-to-line voltage, and VP is the phase-to-neutral voltage. A transformer cannot 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 Transformer or three separate Single Phase Transformers. Consider the circuit below:

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Three Phase Transformer Connections

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.

Three Phase Transformer Star and Delta Configurations But what do we mean by “star” (also known as Wye) and “delta” (also known as Mesh) when dealing with three-phase transformer connections. 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 three available voltages, which themselves are each displaced from the other by 120 electrical degrees, not only decided on the type of the electrical connections used on both the primary and secondary sides, but determine the flow of the transformers currents. 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 individual 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 Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers 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.

Transformer Star and Delta Configurations

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.

Transformer Winding Identification

Primary Secondary Connection Winding Winding

Delta D d

Star Y y

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

Interconnected Z z

We now know that there are four different ways in which three single-phase transformers may be connected together between their primary and secondary three-phase circuits. These four standard configurations are given as: Delta-Delta (Dd), Star-Star (Yy), Star-Delta (Yd), and Delta- Star (Dy). 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.

Transformer Delta and Delta Connections

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. Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers 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 secondary’s as shown.

Transformer Star and Star Connections

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:

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Three-phase Voltage and Current

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

Where again, VL is the line-to-line voltage, and VP is the phase-to-neutral voltage on either the primary or the secondary side. 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 turn’s 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 turn’s ratio becomes:

Star-Delta Turns Ratio

Likewise, for a delta–star (Dy) connected transformer, with a 1:1 turn’s ratio, the transformer will provide a 1:√3 step-up line-voltage ratio. Then for a delta-star connected transformer the turn’s ratio becomes:

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Delta-Star Turns Ratio

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.

Three-phase Transformer Line Voltage and Current

Primary-Secondary Line Voltage Line Current Configuration Primary or Secondary Primary or Secondary

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) and VL is the line-to-line voltage with VP being the phase-to-neutral voltage.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Three Phase Transformer 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 side voltages and currents. Given Data: transformer rating, 50VA, supply voltage, 100v, primary turns 500, secondary turns, 100.

Then the secondary side of the transformer supplies a line voltage, VL of about 35v giving a phase voltage, VP of 20v at 0.834 amperes.

Three Phase Transformer Construction 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.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Three Phase Transformer Construction

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. 3 Phase Transformer versus Bank of 3 Single Phase Transformer

We know that the very basic purpose of Transformer is to transmit power at two different voltage levels. For example, if a generating station is generating electrical power at 21 kV and evacuates it power at 400 kV then a three phase transformer of voltage rating 21 kV / 400 kV is used. But the question which arises here is whether we should opt for a single three phase Transformer or bank of three single phase Transformer? Well, mostly you might have seen a single three phase transformer due to economy. But this does not mean that bank of three single phase transformer is never used. If ever you get a chance to visit 700 MW or 1000 MW power plant, you will see the use of bank of three single phase transformer instead of a single three phase transformer. Generally for a large power generating units, bank of 3 single phase transformer is preferred. The main reason is the size and transportation. Let us take an example for better understanding. Consider a 700 MW generating station where we need to choose a generator transformer (GT) to evacuate power to 400 kV Grid. The size of a single three phase transformer of 823 MVA (700 / 0.85) will be quite high and hence will not be easily transportable from the Transformer factory to the site. Thus for this case, bank of three single phase transformer is used. There are many other advantages of using bank of three single phase transformer like ease in maintenance, less cost of spare inventory requirement etc.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Let us have detailed comparison assuming same rating for both type of transformers.

Bank of 3 Single Phase Transformer Single Three Phase Transformer

It is more expensive due to requirement of 3 It is quite economic due to the use of less iron single phase transformer. 3 single phase core, less volume of tank and hence less volume of transformer means requirement of more iron for . core, oil and accessories.

In such case star or delta connection on HV side This only requires three / four HV Bushings as the requires six different HV Bushings to bring out delta / star connection is done inside the tank of the HV terminals of 3 single phase transformers. transformer.

Space requirement is more for installation. Less space requirement for installation.

It offers greater flexibility in erection and Due to single unit, it doesn’t have any flexibility in installation. erection and installation.

The spare inventory cost is less. Only one single phase transformer is required as spare which is The cost of single three phase transformer as less costly. Suppose a generating station has 2 spare is quite high when compared with a single generating units. For both the generating units unit of single phase transformer. (2xbank of three single phase transformer), only one single phase transformer is required as spare.

The maintenance becomes easier due to separate It is quite difficult to repair and replace. units. Replacement of single unit is also easy.

This is less efficient due to losses in the three It is more efficient and losses are less due to units. The losses are more due to use of more iron lesser requirement of iron core. core.

From the above comparison, it is clear that use of a single three phase transformer offers many advantages and above all it is economic. This is the reason, mostly three phase transformers are used instead of bank of three single phase transformer. However, bank of three single phase transformer is used in large generating units for the reason discussed earlier in the post.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Connection of Three Phase Transformer A verity of connection of three phase transformer are possible on each side of both a single 3 phase transformer or a bank of three single phase transformers.

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

Star-Star Transformer

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

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Delta-Delta Transformer In delta-delta transformer, 1 suffixed terminals of each phase primary winding will be connected with 2 suffixed terminal of next phase primary winding.

If primary is HV side, then A1 will be connected to B2, B1 will be connected to C2 and C1 will be connected to A2. Similarly in LV side 1 suffixed terminals of each phase winding will be connected with 2 suffixed terminals of next phase winding. That means, a1 will be connected to b2, b1 will be connected to c2 and c1 will be connected to a2. If transformer leads are taken out from primary and secondary 2 suffixed terminals of the winding, then there will be no phase difference between similar line voltages in primary and secondary. This delta delta transformer connection is zero degree connection or 0o- connection. But in LV side of transformer, if, a2 is connected to b1, b2 is connected to c1 and c2 is connected to a1. The secondary leads of transformer are taken out from 2 suffixed terminals of LV windings, and then similar line voltages in primary and secondary will be in phase opposition. This connection is called 180o-connection, of three phase transformer.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Star-Delta Transformer Here in star-delta transformer, star connection in HV side is formed by connecting all the 1 suffixed terminals together as common point and transformer primary leads are taken out from 2 suffixed terminals of primary windings.

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

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Delta-Star Transformer

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

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

Star-Zigzag Transformer The winding of each phase on the secondary star in a star-zigzag transformer is divided into two equal halves. Each leg of the core of transformer is wound by half winding from two different secondary phases in addition to its primary winding. Choice between Star Connection and Delta Connection of Three Phase Transformer In star connection with earthed neutral, phase voltage i.e. phase to neutral voltage, is 1/√3 times of line voltage i.e. line to line voltage. But in the case of delta connection phase voltage is equal to line voltage. Star connected high voltage side electrical power transformer is about 10% cheaper than that of delta connected high voltage side transformer.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Let’s explain, Let, the voltage ratio of transformer between HV and 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. In Star-Star Transformer

Voltage difference between HV & LV winding,

In Star-Delta Transformer

Voltage difference between HV & LV winding,

In Delta-Star Transformer

Voltage difference between HV & LV winding,

For 132/33KV Transformer K = 4

Case 1 Voltage difference between HV & LV winding,

Case 2 Voltage difference between HV & LV winding,

Case 3 Voltage difference between HV & LV winding,

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers In case 2 voltage difference between HV and LV winding is minimum therefore potential stresses between them is minimum, implies insulation cost in between these windings is also less. Hence for step down purpose star–delta transformer connection is most economical, design for transformer. Similarly it can be proved that for step up purpose delta-star three phase transformer connection is most economical.

Scott-T Transformer Connection Definition: The Scott-T Connection is the method of connecting two single phase transformer to perform the 3-phase to 2-phase conversion and vice-versa. The two transformers are connected electrically but not magnetically. One of the transformers is called the main transformer, and the other is called the auxiliary or teaser transformer.

The figure below shows the Scott-T transformer connection. The main transformer is centre- tapped at D and is connected to the line B and C of the 3-phase side. It has primary BC and secondary a1a2. The teaser transformer is connected to the line terminal A and the centre- tapping D. It has primary AD and the secondary b1b2

The identical, interchangeable transformers are used for Scott-T connection in which each transformer has a primary winding of Tp turns and is provided with tapping at 0.289Tp, 0.5Tpand 0.866 Tp.

Phasor Diagram of Scott Connection Transformer

The line voltages of the 3-phase system VAB, VBC, and VCA which are balanced are shown in the figure below. The same voltage is shown as a closed equilateral triangle. The figure below shows the primary windings of the main and the teaser transformer.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

The D divides the primary BC of the main transformers into two halves and hence the number of turns in portion BD = the number of turns in portion DC = Tp/2.The voltage VBD and VDC are equal, and they are in phase with VBC.

The voltage between A and D is

The teaser transformer has the primary voltage rating that is √3/2 or 0.866 of the voltage ratings of the main transformer. Voltage VAD is applied to the primary of the teaser transformer and therefore the secondary of the voltage V2t of the teaser transformer will lead the secondary terminal voltage V2m of the main transformer by 90º as shown in the figure below.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

Then,

For keeping the voltage per turn same in the primary of the main transformer and the primary of the teaser transformer, the number of turns in the primary of the teaser transformer should be equal to √3/2Tp.

Thus, the secondary’s of both transformers should have equal voltage ratings. The V2t and V2m are equal in magnitude and 90º apart in time; they result in the balanced 2-phase system.

Position of Neutral Point N The primary of the two transformers may have a four wire connection to a 3-phase supply if the tapping N is provided on the primary of the teaser transformer such that

The voltage across AN = VAN = phase voltage = Vl/√3.

Since the voltage across the portion AD.

the voltage across the portion ND

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers The same voltage turn in portion AN, ND and AD are shown by the equations,

The equation above shows that the neutral point N divides the primary of the teaser transformer in ratio.

AN: ND = 2: 1

Applications of Scott Connection The following are the applications of the Scott-T connection.

1. The Scott-T connection is used in an electric furnace installation where it is desired to operate two single-phase together and draw the balanced load from the three-phase supply. 2. It is used to supply the single phase loads such as electric train which are so scheduled as to keep the load on the three phase system as nearly as possible. 3. The Scott-T connection is used to link a 3-phase system with a two–phase system with the flow of power in either direction.

The Scott-T connection permits conversions of a 3-phase system to a two-phase system and vice versa. But since 2-phase generators are not available, the converters from two phases to three phases are not used in practice.

Open Delta or V-Connection of Transformer As we know, a three phase Transformer bank connected in Delta-Delta when supplies a three phases balanced load then individual Transformers share 1/3 of the total load. But if there is some fault in any one of the Transformer and due this one Transformer is taken out of service, then also three phase power can be supplied though at a reduced power level. The resulting connection obtained after the removal of one of the Transformer from a three phase Transformer bank connected in Delta-Delta is known as an Open Delta or V-connection of Transformer. Figure below depicts this open Delta or V-connection.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

As can be seen from the figure above, one phase in Open Delta or V-connection is missing then how can we deliver three phase power?

Since only two phase voltages are available i.e. Vac and Vbc so we need to calculate the remaining voltage Vab and then only we can judge whether we can supply three phase power or not. Note that for supplying three phase power, the three voltages i.e. Vca, Vbc and Vab must be balanced in the sense that all of them are equal in magnitude and 120° displaced mutually in time domain. Thus to find, Vabwe need to draw voltage triangle first.

From the above voltage triangle, it can be written that

Vab+Vbc+Vca = 0, bold letters mean phasor form.

So, voltage across the open Delta terminal can be found as Vab = Voltage across open delta terminal = – (Vbc+Vca)

Here Vbc and Vca are equal in magnitude, say V but 120° displaced. Therefore their resultant will be V and 120° apart from the reference voltage i.e. Vbc &Vca. Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers Thus we see that Open Delta connection, secondary line voltages form a balanced system and balanced three phase load can be supplied.

Now, we will calculate the amount of VA that can be supplied by an Open Delta connected Transformer.

VA Delivered by Open Delta:

Case1: When all the three transformers of three phase Transformer bank are in service. Suppose, Iph = Phase current of each of Secondary Vph = Phase voltage of each of Secondary Therefore, Line Voltage VL = Vph (because of Delta connection) Line Current IL = 1.732Iph Thus, VA Rating of Bank of three Transformers in Delta = 1.732VLIL = 1.732xVphx1.732xIph = 3VphIph

Case2: Open Delta Connection As in Open Delta connection, only two Transformers are there in service so, VA Rating of Open Delta = 2VphIph

But this is not correct. Why? Because as can be seen from the first figure, Line Voltage in Open Delta VL= Vph Line Current in Open Delta IL= Iph as there is no path to bifurcate the line current. Same current is flowing in line as well as in phases. Therefore, VA Rating of Open Delta = 1.732xVLxIL = 1.732 VphIph

Thus, VA Rating of Open Delta / VA Rating of Close Delta = 1.732VphIph/ 3VphIph =1 / 1.732 =0.577

Thus the VA delivering capacity of Open Delta becomes 57% of that of the full capacity when all the three Transformers are in service. It shall also be noted that, though the total capacity of Transformers in Open Delta is 2VphIphbut still Open Delta can only deliver 1.732VphIph.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers The Ratio of actual available kVA rating to the sum of the kVA rating of installed Transformer is called Utilization Factor and given by

U.F = Ratio of actual available kVA / Sum of the kVA rating of installed Transformer

For Open Delta connection, U.F = 1.732VphIph/ 2VphIph = 0.866

Thus it is beneficial to operate the bank of Transformer in Open Delta at 86% of rated capacity while the faulty Transformer is under maintenance.

Parallel Operation of Three Phase Transformer.

Parallel operation of three phase transformer is very common in three phase power generation, transmission and distribution. It is advantageous to use two or more Transformer units in parallel instead of using a single large unit. This offers flexibility for maintenance as well as operation.

Advantage of Parallel Operation of Three Phase Transformers

 It increases the reliability of supply system. Let us try to understand how this happens. Suppose a fault occurs in any one of the Transformer unit. In such case, the faulty transformer may be taken out of service while the remaining transformers will feed the power supply. If there were only one large transformer unit is installed for supplying the load, the supply to the entire load will be interrupted during breakdown of the transformer. Thus the reliability of supply system is increased by parallel operation of transformers.  The size of transformer increases with the increase of its rating. Therefore, a larger transformer will be bigger in size. Therefore, its transportation form manufacturer to the Site will be difficult. Whereas, transportation and installation of small sized transformers are comparatively easy.  The maintenance opportunity in case of parallel operation is increases. One or more transformers may be taken under maintenance while the remaining transformers will supply the load at reduced power.  Condition for Parallel Operation of Three Phase Transformers

Following are the necessary conditions for parallel operation of 3 phase transformers:

 The line voltage ratio of the transformers must be same.  The transformers should have equal per unit leakage impedance.  The ratio of equivalent leakage reactance to equivalent resistance should be same for all the transformers.  The transformers should have the same polarity.

Department of EEE, DSCE Bangaluru-78 Electrical Machines-1 (19EE3DCEM1) Module-3- Three-phase Transformers

Advantages of Three Phase Transformer over Single Phase Transformer are:  Less cost  Less Weight  less size  Less time require to assembling  Require less space  Deliver more power  Higher efficiency  Easier to install  Easy transportation and installation  Easy to repair  Easy assembling and  Also we can get Single Phase supply from Three Phase supply, while it is not possible to get Three Phase supply from Single Phase Supply. Disadvantages of Three Phase Transformer over Single Phase Transformer are:  Greater cost of standby Units  Increased cost and inconvenience of repairs.  In Single Phase transformer (three Single Phase Transformer) failure of one transformer, the other two, Single Phase Transformer still supply the power, while it is not possible in case of failing a Three Phase Transformer.

Department of EEE, DSCE Bangaluru-78