What is the transformer turns ratio for a step-down transformer with a 4.16kV primary delta connection and a 480/277V wye secondary?

To determine the transformer turns ratio for a step-down transformer with a primary voltage of 4.16 kV (4160 V) in a delta configuration and a secondary voltage of 480/277 V in a wye configuration, you need to look carefully at the voltage levels and how they translate in terms of turns.

The primary voltage of 4.16 kV means that when expressed in volts, it is 4160 V. The secondary voltage of 480 V represents the line-to-line voltage for the wye configuration, which can be compared against the primary voltage directly. In a wye connection, the phase voltage can be calculated from the line-to-line voltage, but for the turns ratio calculation, the line-to-line voltage is directly compared to the primary.

The transformer turns ratio (TRN) can be calculated using the formula:

[ \text{TRN} = \frac{\text{Primary Voltage}}{\text{Secondary Voltage}} ]

Now plugging in the numbers:

[ \text{TRN} = \frac{4160 , \text{V}}{480 , \text{V}} ]

Calculating this gives:

[ \text{TRN} = \frac{4160