Open-Delta or V-V Connection of Transformer

Open-Delta or V-V Connection of Transformer

An open-delta or V-V connection is used to supply a three-phase load with a two-phase supply.

When three single-phase transformers are connected in a delta-delta connection, and one transformer is unable to operate or damaged, the supply to the load is given by the remaining two single-phase transformers. This type of connection is known as Open-delta or V-V connection.

The open-delta connection is a temporary solution to supply three-phase load in emergency conditions.

Let’s consider a delta-delta connected transformer. The connection diagram of the delta-delta connection is shown in the figure below.

Delta-Delta Connection of Transformer
Delta-Delta Connection of Transformer

If one transformer is unable to operate or in maintenance, the remaining two transformers operate on reduced load conditions, as shown below.

Open-Delta Connection of Transformer
Open-Delta Connection of Transformer

In an open-delta connection, two out of three transformers are working; however, it does not mean that this type of connection gives two-thirds or 66% efficiency.

The Open-delta connection gives 58% efficiency of full-load delta-delta connections. To prove this, we need to compare the VA ratings of delta-delta or open-delta connections.

For delta-delta connection;

    \[ S_{dd} = \sqrt{3} V_L I_L \]

In delta connection, line current is √3 times of phase current.

    \[ I_L = \sqrt{3} I_{ph} \]

    \[ S_{dd} = \sqrt{3} V_L \sqrt{3} I_{ph} \]

    \[ S_{dd} = 3 V_L I_ph \]

For open-delta connection;

    \[ S_{vv} =  \sqrt{3} V_L I_L \]

    \[ S_{vv} =  \sqrt{3} V_L I_{ph} \]

Now, take a ratio of both connections;

    \[ \frac{ S_{dd}}{ S_{vv}} = \frac{\sqrt{3} V_L I_{ph}}{3 V_L I_ph } \]

    \[ \frac{ S_{dd}}{ S_{vv}} = \frac{1}{\sqrt{3}} \]

    \[ \frac{ S_{dd}}{ S_{vv}} = 0.577 \approx 0.58 \]

Hence, it is proved that, the load carried by open-delta connection is 58% of the load taken by the delta-delta connection.

Now, we need to check the phase difference in output. As shown in above figure, there is no connection between point a and c. But there is some potential difference.

    \[ V_{ac} + V_{bc} + V_{ca} = 0 \]

(1)   \begin{equation*} V_{ca} = -V_{ab} - V_{bc} \end{equation*}

In delta-delta connection, we consider balanced power and take AB as reference.

    \[ V_{AB} = V_P \angle 0^\circ \]

    \[ V_{BC} = V_P \angle -120^\circ \]

    \[ V_{CA} = V_P \angle +120^\circ \]

Where VP is a magnitude of line voltage at primary side.

If we neglect the leakage impedances, then we can write;

    \[ \[ V_{ab} = V_S \angle 0^\circ \]

    \[ \[ V_{bc} = V_S \angle -120^\circ \]

Where VS is a magnitude of line voltage at secondary side.

Now, put the above values in equation-1;

    \[ V_{ca} = - V_S \angle 0^\circ - V_S \angle -120^\circ \]

    \[ V_{ca} = - V_S - (-0.5 V_S - j 0.866 V_S) \]

    \[ V_{ca} = -0.5 V_S + j 0.866 V_S \]

    \[ V_{ca} = V_S \angle +120^\circ \]

So, it is clear that the voltage is equal and 120˚ apart in time and balanced three-phase line voltages available in V-V connection.

When the transformer is connected in an open-delta connection, the efficiency is reduced to 58%. For example, 30 kVA three single-phase transformers (10 kVA each) are used in delta-delta connections.

For any reason, one out of three transformers is damaged, and the transformer is operated in an open-delta connection to supply the three-phase load.

Now, the capacity of the transformer is reduced by 58%. So, in this example,

    \[ 30 kVA \times 0.58 = 17.4 kVA \]

Therefore, the remaining two transformers are used to take a load of 17.4 kVA. It means ten kVA each (total 20 kVA) transformers are used to take a load of 17.4 kVA.

So, the unitality factor of this connection is 20/17.4 = 0.866.

Then also, instead of delta-delta connection, the transformers used in the open-delta connection express overload on each transformer about 73.2%.

    \[ \frac{Total \, load \, in \, V-V}{VA \, rating} = \frac{\sqrt{3}V_L I_S}{V_L I_S} = \sqrt{3} = 1.732 \]

This overload may be carried out temporarily. But some provisions must be taken to reduce the load. It may cause overheating, and consequent breakdown of the remaining two transformers must be avoided.

 Limitation of Open-delta Connection

The limitations of open-delta connections are listed below.

  • In an open-delta connection, two transformers are used to supply a three-phase load. In this condition, both transformers operate on different power factors.
  • Secondary terminal voltages become unbalanced (due to leakage impedance).
  • Reduction in power handling capacity of transformers. For example, two transformers are used instead of three. So, efficiency reduced to 2/3 = 0.6667 = 66.67%. But in an open-delta connection, the efficiency is 57.7%.

    \[ \frac{66.67-57.7}{57.7}\times 100 = 15.5% \]

Therefore, the efficiency of the transformer was reduced to 15.5%.

Scott Connection of Transformer

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