# 3 Phase Transformer Input Line Current (Δ-Y)

• jegues
In summary, the given conversation discusses a 25 MVA, 69kV/660V 60Hz, Δ-Y connected three-phase power transformer with various parameters referred to the HV side. The transformer delivers 20MVA to a three-phase load with a power factor of 0.866 lagging at 660V. The conversation also includes questions about determining the input line-to-line voltage, input line current, and real and reactive power input to the transformer. The attempted solution involves converting the three-phase circuit into its Y-Y equivalent and solving for the single phase circuit on the HV side. The correct value for the input line current is found to be (1/3) of the claimed line current, and the real and
jegues

## Homework Statement

A 25 MVA, 69kV/660V 60Hz, Δ-Y connected three-phase power transformer has an equivalent series impedance of 2.28 + j17.15Ω, a croe loss resistance of 15235.2Ω and a magnetizing reactance of 5078.4Ω all referred to the HV side. The transformer delivers 20MVA to a three-phase load with 0.866 lagging power factor at 660V.

b)Determine the magnitude of the input line-to-line voltage.

c)Determine the input line current.

d)Calculate the real and reactive power input to the transfromer

## The Attempt at a Solution

Please see the figures attached for my attempt at the solution.

My strategy was to conver the 3 phase circuit into its Y-Y equivalent, and solve the single phase circuit on the HV side.

I am getting confused with how to find the input line voltage and current.

I was able to transfer everything to the HV side of the single phase circuit and solve for every voltage and current.

Since the HV side was turned into a Y equivalent circuit it leads me to believe that the input voltage is simply √(3)*input phase voltage I solved(i.e. Vshv) and the input line current should be the same as the phase current I solved.(i.e. Ishv)

Well it turns out I am correct for the input line voltage, but incorrect for the input line current.

It just so happens that the correct value of the input line current is (1/3) of my claimed line current. (i.e. Ishv)

Why is this? What am I discounting?

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I am still confused about the real and reactive power input to the transformer.From what I can tell it should be (1/3) of the real or reactive power of the single phase circuit. Is this correct?

## 1. What is a 3 phase transformer?

A 3 phase transformer is an electrical device that is used to transfer electrical energy between three different circuits, typically at different voltages. It consists of three sets of primary and secondary windings that are connected in a specific configuration to step up or step down the voltage.

## 2. What is the difference between a Δ and Y connection in a 3 phase transformer?

A Δ (delta) connection refers to a transformer where the primary and secondary windings are connected in a closed loop or triangle shape. A Y (wye) connection refers to a transformer where the primary and secondary windings are connected in a Y shape. These connections affect the voltage and current in each winding and determine the transformer's overall output.

## 3. How is input line current calculated in a 3 phase transformer?

The input line current in a 3 phase transformer can be calculated using the formula I = (kVA x 1000) / (√3 x V), where I is the input line current in amps, kVA is the transformer's apparent power rating, and V is the voltage of the primary winding. This formula takes into account the transformer's efficiency and the power factor of the load.

## 4. What is the significance of input line current in a 3 phase transformer?

The input line current is an important parameter in a 3 phase transformer as it determines the amount of current that the transformer draws from the source and the amount of current that is delivered to the load. It is also used to calculate the size of the wires and other components needed for the transformer's installation.

## 5. How does the input line current change with different loads in a 3 phase transformer?

The input line current in a 3 phase transformer varies with the load. As the load increases, the input line current also increases. This is because the load demands more power, which in turn causes the transformer to draw more current from the source. Similarly, as the load decreases, the input line current also decreases.

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