# Open Delta Connection of Transformer

When two single phase transformer is connected in open delta connection the arrangement can provide three phase supply to the load. The open delta connection of transformer is also known as V-V connection.

The closed delta connection of transformer provides the three phase supply when connected to the balanced load with individual sharing of 1/3 of the load. If one of the delta winding gets opened the transformer can still be operated with two phase delta winding. The connection diagram of the open delta connection of the transformer is as shown below.

Thevenin's theorem with solved ...
Thevenin's theorem with solved examples
The efficiency of the open delta connection is lower than the closed delta connection. However, the transformer can be operated with reduced efficiency in the open delta or V- V connection. Let us discuss how the transformer delivers three phase power in open delta connection when one of the phase is missing. Two of the phases Vab and Vbc is available and Vac is missing. The vector sum of all the three phase voltage is zero. Therefore,  the voltage across open delta terminal is ;
Vca = – ( Vab + Vbc)

The phasor diagram of open delta connection is as shown in below figure.

Vab and Vbc are equal in magnitude, therefore the resultant will be equal to V and 120 degree apart from the reference voltage Vab and Vbc. From this it is clear that the open delta connection can supply the three phase supply to the load. If one of the transformer of delta connected transformers gets open and the load on the transformer is the same, the transformer gets overloaded. In this case, the load on the transformer needs to be reduced in order to avoid overloading. The VA rating of the transformer in open delta connection gets reduced as compared to the  VA rating of the closed delta connection of transformer.

When we feed three phase supply to  open delta transformer, the both the transformer operates at different power factor. One transformer operates at (30-Φ)power factor and other transformer operates at (30+Φ)power factor.

The active power delivered by one transformer is KVA Cos(30-Φ)the active power delivered by other transformer connected in open delta configuration is KVACos(30+Φ).

Case 1
When  all the three winding of transformer in the circuit
Let,
Vph – Phase Voltage of each secondary
Iph  – Phase current of each secondary
In closed delta connection the line voltage is equal to the phase voltage.
VL = Vph
VA rating of the closed delta transformer
=  √3 VL IL
=  1.732 Vph  x √3 Iph
= 1.732 Vph x 1.732 Iph
= 3 Vph Iph
Case 2
Open Delta Connection

In a closed delta connection the line current is 1.732 times of the phase current, but in open delta connection the line current is equal to the phase current. The phasor diagram of the open delta transformer is as given below.

VA rating of the open delta transformer ;

VA rating of open delta transformer can be calculated as follows.

The KW rating of the open delta transformer is;

=VphIph Cos(30-Φ) + VphIph Cos(30-Φ)
= Vph Iph[ Cos(30-Φ)+Cos(30-Φ)]

Vph Iph[ 2Cos30 CosΦ]
=Vph Iph[ 2 x√3/2 CosΦ]
Vph Iph[ √3 CosΦ]
√3 Vph Iph CosΦ
3 Vph IphCosΦ   ——(1)

From equation(1),the VA rating of the open delta transformer is;

3 Vph Iph
=  1.732 Vph  x  Iph
= 1.732 Vph Iph

## Open Delta Maximum Power Vs standard 3 Phase Delta Maximum PowerThe relationship between VA rating of open delta and close delta connection is as follows.

VA rating of Open Delta / close Delta From above it is clear that the VA delivering capacity of the open delta transformer is 57.7 % of the VA delivering capacity when all the three transformers are connected in delta.

The total VA available when the two transformer is connected in delta connection is 2 Vph Iph. However, the actual VA delivery of  the open delta connection is 1.732 Vph Iph.

Transformer Utility Factor(TUF)
The ratio of actual VA available to the total VA available in open delta connection is known as the transformer utility factor(TUF). Examples:
Suppose the load VA demands is 60 VA. What will be the rating of each transformer if connected

• Closed Delta Connection
• Open Delta Connection

If all three transformer is connected in closed delta connection the VA delivered by each transformer is 60/3 = 20 VA, therefore the VA rating of each transformer  is 20 VA.

If one of the transformer is removed from the closed delta and two transformer are connected in the open delta connection then the total VA delivery will be  60 x 0.557= 33.42VA and each  transformer will deliver 33.42/2=16.71 VA. The circuit load is 60 VA, hence the 20 VA transformers connected in open delta connection can’t deliver 60 VA to the load.The new VA rating of the transformers for open delta connection to deliver 60 VA  will be equal to 60/0.557=107.71 VA.Thus the each transformer VA rating in open delta connection to deliver 60 VA to load will be 107.71/3=35.90 VA.

Two single phase transformers of rating 100 KVA are connected in open delta connection. Calculate the maximum VA rating of eah transformer when connected in open delta connection?

Total VA rating of both the transformer= 100+100= 200 KVA
The transformer utility factor = 0.866
VA rating of open delta transformer = TUF x Total VA rating
VA rating of open delta transformer =0.866 x 200= 173.2 KVA
VA rating of each transformer =173.2/2 = 86.6 KVA

Two single phase transformers of rating 500 KVA are connected in open delta connection. Calculate the maximum VA delivering capacity of the open delta transformer.

If three transformer of 500 KVA rating are connected in close delta, the maximum VA delivery = 3 x 500 = 1500 KVA

If one of the transformer is removed and the rest two transformers are connected in open delta, the VA delivery of the transformer

=0.577 x (VA delivery of the close delta connected transformers )
=0.577  x 1500
= 865.5 KVA

VA capacity of each transformer =865.5/2 = 432.75 KVA

Alternate method:

VA rating of each transformer in open delta
= TUF x VA rating of each transformer
= 0.866 x 500
= 432.75

Two single phase transformers of rating 15MVA,4160 V are connected in open delta connection to form a three phase transformer. Calculate the maximum power that this transformer can deliver.

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