In order to meet an cmergency, three single-phase...

In order to meet an cmergency, three single-phase transformers with $12,470 / 7200 \mathrm{V} \mathrm{rms}$ are connected in $\Delta-\mathrm{Y}$ to form a three-phase transformer which is fed by a $12,470-\mathrm{V}$ transmission line. If the transformer supplies $60 \mathrm{MVA}$ to a load, find: (a) the turns ratio for each transformer, (b) the currents in the primary and secondary windings of the transformer, (c) the incoming and outgoing transmission line currents.

In order to meet an cmergency, three single-phase transformers with $12,470 / 7200 \mathrm{V} \mathrm{rms}$ are connected in $\Delta-\mathrm{Y}$ to form a three-phase transformer which is fed by a $12,470-\mathrm{V}$ transmission line. If the transformer supplies $60 \mathrm{MVA}$ to a load, find:
(a) the turns ratio for each transformer,
(b) the currents in the primary and secondary windings of the transformer,
(c) the incoming and outgoing transmission line currents.

Key Concepts

Apparent Power and Current Calculations in Three-Phase Systems

Apparent power (measured in MVA) in a three-phase system relates the system voltage and current through the formula S = ?3×V_line×I_line. Understanding this relationship is essential for determining the currents in the transformer’s primary and secondary windings as well as the transmission line currents. The concept ensures that power ratings, voltage levels, and current flows are consistently and correctly computed for both single and three-phase calculations.

Transformer Turns Ratio

This concept involves the ratio of the number of turns in the primary winding to the number of turns in the secondary winding of a transformer. It determines how the input (primary) voltage is scaled to match the output (secondary) voltage. In analysis, the turns ratio is directly obtained from the specified transformer ratings and is crucial for understanding the voltage transformation and designing appropriate transformer windings.

Delta-Wye Transformer Connection

A Delta-Wye connection is a configuration where the primary winding is connected in a delta formation and the secondary winding in a wye (star) formation. This configuration affects the relationship between line and phase voltages and currents. The delta connection can provide a phase shift and handle unbalanced loads, while the wye connection provides a neutral point, and the differences between line and phase values must be carefully considered when analyzing such transformer systems.

Three-Phase System Line and Phase Relationships

In three-phase systems, it is essential to distinguish between line and phase voltages and currents. In delta connections, the line voltage equals the phase voltage and the line current is ?3 times the phase current, while in wye connections, the line voltage is ?3 times the phase voltage and the line current equals the phase current. This concept is key for calculating the actual current levels in the transformer windings and the transmission lines based on the system configuration.

Transcript

0:00 Hello everyone.

00:01 Let us do the following question.

00:03 We have to, in the question it is said that in order to meet an emergency, the single -phase transformer with 1 -2 -470 divided by 7200 -volt rms are connected in a delta -y form, are connected in a delta -form, three -phase transformer, which is fed by a 1 -2470 -volt transmission line.

00:27 If the transformer supplies 60 millivolt to a road, we have to find the turn ratio, the current in the primary and scannery, and the incoming and outgoing transmission line circuit.

00:41 Firstly we will consider it.

00:43 We will say that consider just one face as a time.

00:48 Consider just one face at a one face at a time.

00:56 We will consider at first only one phase.

00:59 If we will solve this, this is the structure we will get for one phase.

01:04 If now we will solve this number of terms, we will write this vl under the root 3, v into lp.

01:12 This can be written as 70200 divided by 1 to 470 under the root 3.

01:20 Value of this can be written as 1 by 3.

01:23 Value of this can be written as 1 by 3.

01:26 Next we have to find the load carried by each transformer.

01:30 So we will say the load carried by each transformer is the load carried by each transformer is 60 by 3.

01:45 This can be written as 20 mega volt ampere...