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7.11 Single-Phase Equivalent Circuit

Let's take the transformer shown in Fig. 7.28, which has its primary (high voltage) connected in delta and its secondary (low voltage) in star with the accessible neutral (Dyn).

Diagram of a three-phase transformer connection. The left side shows a wye (Y) configuration with terminals labeled T, S, N, and R. The right side displays a delta (Δ) configuration with terminals labeled R, S, and T. The diagram illustrates the electrical connections between the two configurations.

Fig. 7.28 Delta to star transformer connection.

As previously mentioned, in a star connection, the star always tries to equalize the current, and we get two voltage levels that can connect a single-phase load. It is expressed as:

IL = IP, and VL = 3·VP (7.39)

And delta tries to equalize the voltage. It is used in equal voltage situations like motors etc. It is expressed as:

IL = 3·IP and: VL = VP (7.40)

Note that in the star connection, the current that flows through the line (IL) is the same as the phase current (Ip). The current in the line (IL) equals the phase current (IP); while the line voltage (VL) is the square root of 3 phase voltages (VP).

In the delta connection, the line voltage (VL) is the same as the phase voltage (VP). The line current (IL) is the square root of 3—phase voltage (IP).

练习题

In a three-phase transformer with Dyn connection, how are the primary and secondary windings configured?

A. Primary in star, secondary in delta

B. Primary in delta, secondary in star with accessible neutral

C. Both primary and secondary in delta

D. Both primary and secondary in star

In a star-connected three-phase system, if the phase voltage $V_{P} = 230 V$ , what is the line voltage $V_{L}$ ?

230 V

400 V

690 V

133 V

In a delta-connected three-phase system, what is the relationship between line current $I_{L}$ and phase current $I_{P}$ ?

I_{L} = I_{P}

I_{L} = 3 \times I_{P}

I_{L} = 3 \times I_{P}

I_{L} = I_{P} / 3

Which of the following statements correctly describe the characteristics of star and delta connections in three-phase systems?

A. Star connection provides two voltage levels suitable for single-phase loads

B. Delta connection is commonly used for motors due to equal voltage across windings

C. In star connection, line current equals phase current

D. In delta connection, line voltage equals phase voltage

E. Star connection tries to equalize voltage

In a star-connected three-phase system, the line current $I_{L}$ is equal to the phase current $I_{P}$ .

In a delta-connected three-phase system, the line voltage $V_{L}$ is $3$ times the phase voltage $V_{P}$ .

A Dyn transformer has its high-voltage primary winding connected in star and its low-voltage secondary winding connected in delta.

In a star connection, the line voltage is ___ times the phase voltage.

In a delta connection, the line current $I_{L}$ equals ___ times the phase current $I_{P}$ .

Why is a star-connected secondary winding advantageous when single-phase loads need to be supplied?

A Dyn transformer has its primary winding connected in delta and its secondary winding connected in star with an accessible neutral. If the line voltage on the primary (delta) side is 11 kV, what is the phase voltage across each primary winding?

A. 11 kV

B. 6.35 kV

C. 19.1 kV

D. 33 kV

Which of the following statements correctly describe the characteristics of a star-connected secondary winding in a Dyn transformer?

A. The line current equals the phase current (

I_{L} = I_{P}

)

B. The line voltage equals

3

times the phase voltage (

V_{L} = 3 \cdot V_{P}

)

C. All phases connect to a common terminal known as neutral

D. The line voltage equals the phase voltage (

V_{L} = V_{P}

)

E. Two voltage levels are available for connecting single-phase loads

In a three-phase transformer with a delta-connected primary and star-connected secondary (Dyn configuration), the delta connection on the primary side is advantageous for motor applications because it equalizes the voltage, while the star-connected secondary provides two voltage levels suitable for single-phase loads.

In a Dyn transformer, the primary winding uses a _ connection where the line voltage equals the phase voltage, while the secondary uses a star connection where the line current equals the _ current.

Explain why a star-connected secondary winding with an accessible neutral in a Dyn transformer is beneficial for supplying both three-phase and single-phase loads.

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7.11 Single-Phase Equivalent Circuit