Transformer Equivalent Reactance Quiz

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Questions and Answers

What is the equivalent reactance of the transformer referred to its HV side?

0.61 Ω/phase

2.76 Ω/phase

1.82 Ω (correct)

0.8 Ω/phase

What is the line-to-line voltage applied to the primary terminals of the transformer?

2400 V

24000 V (correct)

1200 V

240 V

Which transformer connection is at the input side of the system described?

Y-Δ (correct)

Y-Y

Δ-Y

Δ-Δ

How is the total current calculated at the receiving end transformers when a short circuit occurs?

By dividing the phase voltage by the total impedance Signup and view all the answers

What is the calculated steady-state short circuit current at the LV terminals?

5940 A Signup and view all the answers

What is the per phase equivalent circuit reactance referred to the 2400 V side for the first transformer?

j 0.92 Ω Signup and view all the answers

What is the phase voltage applied to the primary side of the transformer?

$1385 V$ Signup and view all the answers

Which of the following statements about transformer connections is correct?

A Y-Δ connection involves a primary and secondary with different voltage levels. Signup and view all the answers

What is the output voltage across the load when a balanced 3φ load is connected to the transformers?

2329 V Signup and view all the answers

What transformation ratio is used for converting from Y-connection to Δ-connection?

√3:1 Signup and view all the answers

If the impedance of the feeder is given as 0.0005+j0.002 Ω/phase, what is its equivalent when squared with the transformation ratio?

0.15 + j0.6 Ω Signup and view all the answers

What is the rated phase current drawn by the load at a power factor of 0.80 lagging?

20.8 A Signup and view all the answers

In the equivalent circuit, if the line voltage is 2400 V, what is the per-phase voltage in the Y-connection?

232.9 V Signup and view all the answers

What is the reactance of the feeder per phase in the given problem?

0.002 Ω Signup and view all the answers

What type of transformer connection is assumed for the load when no specification is provided?

Y-Y Signup and view all the answers

How does the described power factor of 0.80 lagging affect the current supplied by the transformers?

It causes the current to lag behind the voltage. Signup and view all the answers

What is the formula for calculating voltage regulation in a transformer?

VR = (VNL - VFL) / VFL × 100% Signup and view all the answers

Which test is used to determine the equivalent circuit parameters for a transformer?

Open Circuit Test Signup and view all the answers

How is the copper loss in a transformer calculated at full load?

Pcopperloss = I^2 * Req Signup and view all the answers

The equivalent resistance in the short circuit test can be expressed as which formula?

Zeq = Req + jXeq Signup and view all the answers

In the open circuit test, what does the parameter YOC represent?

The susceptance of the circuit Signup and view all the answers

The core loss in a transformer is primarily composed of which type of loss?

Eddy current loss Signup and view all the answers

What represents the maximum efficiency condition for the transformer?

Pcu = Pcoreloss Signup and view all the answers

Which factor primarily affects the reactance calculations of the transformer?

Frequency Signup and view all the answers

For a transformer with a turns ratio of 26.4 based on the example, what is its primary to secondary voltage ratio?

6600V/250V Signup and view all the answers

What is the effect of a power factor of 0.8 lagging on the voltage regulation calculation?

It requires adjustment in current calculations Signup and view all the answers

During the open circuit test, which of the following values is used to calculate equivalent resistance?

Voc Signup and view all the answers

How is the induced voltage at primary side referred?

Vp = V2 + I2Zeq Signup and view all the answers

The equivalent circuit parameters, when referred to the primary, include which resistances?

Req and Xeq Signup and view all the answers

Study Notes

Transformer and Circuit Overview

Equivalent reactance of each transformer referred to its high-voltage (HV) side is 1.82 Ω.
All circuit resistances are neglected for simplicity.
The transformer rating is 500 kVA with a 24000:2400V (HV to low voltage) line-to-line voltage (Y-Δ connection).
Sending end transformers have an equivalent reactance of 2.76 Ω/phase referred to the 2400V side.
Voltage applied to the primary terminals is 24000V line-to-line.

Short Circuit (SC) Analysis

Steady-state short circuit occurs at the 240V terminals of the receiving-end transformers.
Equivalent impedance for the sending end can be calculated per phase.
Sending end voltage per phase at the primary (2400V side) is approximately 1385V.

Current Calculations

SC current at HV (short-circuit phase current) calculated as 594 A (angle -90°) based on the total impedance.
Line current for the low voltage (LV) or secondary side is 5940 A when referring to the transformer turns ratio.

Transformer Measurements

Inrush current may occur during transformer energizing.
Calculating parameters includes open circuit (OC) and short circuit (SC) tests.
OC test: Determines magnetizing and core losses; applicable metrics include voltage, current, and power readings.
SC test: Used for determining input impedance values through measured current and voltage.

Efficiency and Voltage Regulation

Voltage regulation (VR) is calculated by the change in no-load (NL) and full-load (FL) voltages divided by the full-load voltage.
Efficiency (η) is calculated by relating output power to total power including losses from copper and core.
Maximum efficiency occurs at a certain load condition where copper losses equal core losses.

Example Calculations

A 1000 kVA single-phase transformer example showcases OC and SC test results, aiding in equivalent circuit determination.
Voltage regulation at full load with a power factor of 0.8 lagging is analyzed to be approximately 4.24%.
This includes determining output power and losses during operation at specified parameters.

Load Considerations

The system supplies a balanced three-phase load through a feeder with specific impedance characteristics.
Line-to-line voltage seen at the load while drawing rated current at a 0.80 lagging power factor is crucial for understanding performance.
Equivalent impedance for the feeder is derived from the circuit analysis involving the rated current and voltage drops.

Final Notes on Transformer Connection Types

Transformers may utilize different connections: Y-Δ or Δ-Δ, affecting voltage and current transformations.
Equivalent circuit parameters vary based on whether losses are considered or if simplifying assumptions are made for circuit analysis.

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Description

Test your understanding of transformer equivalent reactance and three-phase systems with this quiz. It covers topics such as transformer connections, reactance calculations, and fault conditions. Assess your knowledge on how these elements interact in electrical engineering.