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

The closed delta connection of the 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 shown below.

The efficiency of the open delta connection is lower than that of 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 an open delta connection when one phase is missing. Two phases, Vab and V_{bc,} are available, and Vac is missing. The vector sum of all the three-phase voltage is zero. Therefore, the voltage across the open delta terminal is ;

Vca = – ( Vab + Vbc)

The phasor diagram of the open delta connection is shown below.

V_{ab }and V_{bc} are equal in magnitude. Therefore, the resultant will be equal to V and 120 degrees apart from the reference voltage V_{ab} and V_{bc}. From this, it is clear that the open delta connection can supply the three-phase supply to the load. If one of the transformers 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 to avoid overloading. The VA rating of the transformer in the open delta connection gets reduced compared to the VA rating of the closed delta connection of the transformer.

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

The active power delivered by one transformer is kVA Cos(30-Φ), and the active power delivered by another transformer connected in an open delta configuration is kVACos(30+Φ).

**Case 1**–**When all three windings of the transformer in the circuit**

Let,

Vph – Phase Voltage of each secondary

Iph – Phase current of each secondary

In a closed delta connection, the line voltage is equal to the phase voltage.

**VL = Vph**

**VA rating of the closed delta transformer**

= √3 V_{L} I_{L}= 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 the phase current, but in an open delta connection, the line current is equal to the phase current. The phasor diagram of the open delta transformer is given below.

**VA rating of the open delta transformer ;**

VA rating of the 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 Iph**CosΦ ——(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 Power**

The relationship between the 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 three transformers are connected in the delta.

The total VA available when the two transformers are connected in a delta connection is 2 Vph Iph. However, the actual VA delivery of the open delta connection is 1.732 V_{ph }Iph.

**Transformer Utility Factor(TUF)**

The ratio of actual VA to the total VA available in an open delta connection is known as the transformer utility factor(TUF).

**Solved Problems on the Open Delta Connection of the Transformer**

**Problem 1:**

** ****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 transformers are connected in a 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 transformers is removed from the closed delta and two transformers are connected in the open delta connection, 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 an 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, each transformer VA rating in an **open delta connection to deliver 60 VA to load will be 107.71/3=35.90 VA.**

**Problem 2:**

**Two single-phase transformers of rating 100 KVA are connected in an open delta connection. Calculate the maximum VA rating of each transformer when connected in an 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**

**Problem 3:**

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

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

If one of the transformers is removed and the other two transformers are connected in an 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

**Problem 4:**

*Two single-phase* transformers rated 15MVA and 4160 V are connected in an open delta to form a three-phase* transformer. Calculate the maximum power that this transformer can deliver.*

my question is: in open delta voltage transformers used to feed protection relay -neutral displacement protection, if one phase shorted with earth how much the voltage will appear on Va,Vn terminals of open delta in that moment?