A three-phase transformer has 600 primary turns and 200 secondary turns. If the supply voltage is 1000 V, find the secondary line voltage on no-load when the windings are connected in star–delta.
192.45 V
Three-Phase Transformer Star-Delta Voltage Calculation
Let's calculate the secondary line voltage of the three-phase transformer based on the given information.
We are given:
- Primary turns, \(N_p = 600\)
- Secondary turns, \(N_s = 200\)
- Primary supply line voltage, \(V_{p,line} = 1000\) V
- Winding connection: Primary is Star (Y), Secondary is Delta (\(\Delta\))
We need to find the secondary line voltage, \(V_{s,line}\), on no-load.
First, let's consider the primary winding which is connected in Star (Y). In a star connection, the relationship between line voltage and phase voltage is:
\[V_{line} = \sqrt{3} \times V_{phase}\]So, the primary phase voltage \(V_{p,phase}\) is:
\[V_{p,phase} = \frac{V_{p,line}}{\sqrt{3}} = \frac{1000}{\sqrt{3}}\]Next, the ratio of phase voltages in a transformer is equal to the ratio of turns:
\[\frac{V_{p,phase}}{V_{s,phase}} = \frac{N_p}{N_s}\]We can use this to find the secondary phase voltage \(V_{s,phase}\):
\[V_{s,phase} = V_{p,phase} \times \frac{N_s}{N_p}\] \[V_{s,phase} = \left(\frac{1000}{\sqrt{3}}\right) \times \left(\frac{200}{600}\right)\] \[V_{s,phase} = \left(\frac{1000}{\sqrt{3}}\right) \times \left(\frac{1}{3}\right)\] \[V_{s,phase} = \frac{1000}{3\sqrt{3}}\]Finally, let's consider the secondary winding which is connected in Delta (\(\Delta\)). In a delta connection, the relationship between line voltage and phase voltage is:
\[V_{line} = V_{phase}\]So, the secondary line voltage \(V_{s,line}\) is equal to the secondary phase voltage \(V_{s,phase}\).
\[V_{s,line} = V_{s,phase} = \frac{1000}{3\sqrt{3}}\]Now, let's calculate the numerical value:
\[V_{s,line} = \frac{1000}{3 \times \sqrt{3}} \approx \frac{1000}{3 \times 1.73205} \approx \frac{1000}{5.19615} \approx 192.45 \text{ V}\]Therefore, the secondary line voltage on no-load is approximately 192.45 V.
Important Questions from Three Phase Transformer Basics
The core of a three-phase, 50 Hz, 1000/400 V delta/star: 300 kVA core type transformer operated with a flux of 0.04 wb. Find the EMF per turn.
In Three Phase Transformer, The load Current is 139.1 A, and Secondary Voltage is 415 V. The Rating of the Transformer would be:
Three-phase transformer contains-
Three impedances, each of (3−4j) Ω, are connected in delta to a 200 V, three-phase, 50 Hz balanced supply. What are the values of line current and phase current, respectively, in the delta-connected load?
The most familiar application of zigzag transformer is
