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Step1/2

Solution : Complete solution: Background: A three-phase transformer is a type of transformer that is used to transform electrical power in three-phase power systems. It is designed to work with three-phase electrical power, which is a type of AC power that consists of three different phases that are 120 degrees out of phase with each other. Three-phase power is commonly used in power generation and distribution, as well as in many industrial applications. Parallel operation of transformers is a technique used to increase the power handling capacity of transformers. When two or more transformers are connected in parallel, they share the load and distribute the power among themselves. This technique is commonly used in power distribution systems to increase reliability and availability. Design: The design of a three-phase transformer is similar to that of a single-phase transformer. The primary and secondary windings are wound on a core made of laminated steel, which reduces eddy current losses. The windings are typically arranged in a delta or wye configuration. To design a three-phase transformer, the following parameters must be taken into consideration: Rated voltage Rated current Rated power Impedance Turns ratio The turns ratio is used to determine the voltage transformation ratio of the transformer. The voltage transformation ratio is the ratio of the secondary voltage to the primary voltage. When designing a transformer for parallel operation, the following additional parameters must be taken into consideration: Voltage ratio Phase angle Polarity

Explanation

The voltage ratio must be the same for all transformers in parallel, and the phase angles and polarity must be the same. Otherwise, the transformers will not share the load evenly and may cause damage to the system.

Explanation: Please refer to solution in this step.

Step2/2

Calculation: Calculations for three-phase transformers are similar to those for single-phase transformers. The following are some examples of calculations for three-phase transformers: Example 1: A three-phase transformer has a rated power of 150 kVA and a voltage ratio of 480 V/208 V. Calculate the rated current of the transformer. Solution: The rated current can be calculated using the formula: \( \mathrm{{I}=\frac{{S}}{\sqrt{{{3}×{V}}}}} \) Where I is the rated current, S is the rated power, and V is the rated voltage. Substituting the given values, we get: \( \mathrm{{I}=,\frac{{{150},{000}}}{\sqrt{{{3}×{480}}}}} \) I = 182.3 A

Explanation

Therefore, the rated current of the transformer is 182.3 A.

Example 2: Two three-phase transformers are connected in parallel. Transformer A has a rated power of 100 kVA and a voltage ratio of 480 V/240 V, while transformer B has a rated power of 150 kVA and a voltage ratio of 480 V/240 V. Calculate the total rated power of the transformers in parallel. Solution: The total rated power of the transformers can be calculated by adding the rated powers of the individual transformers: Total rated power = 100 kVA + 150 kVA Total rated power = 250 kVA Therefore, the total rated power of the transformers in parallel is 250 kVA. Example 3: Two three-phase transformers are connected in parallel. Transformer A has a rated power of 100 kVA and a voltage ratio of 480 V/240 V, while transformer B has a rated power of 150 kVA and a voltage ratio of 480 V/240 V. Calculate the total rated current of the transformers in parallel. Solution: The total rated current of the transformers can be calculated using the formula: \( \mathrm{{I}=\frac{{S}}{\sqrt{{{3}×{V}}}}} \)

Explanation

Where I is the rated current, S is the rated power, and V is the rated voltage.

For transformer A: \( \mathrm{{I}=\frac{{{100},{000}}}{\sqrt{{{3}×{480}}}}} \) Operation: When two or more transformers are connected in parallel, they should share the total load current in proportion to their respective kVA ratings. However, due to manufacturing and design differences, some transformers may have slightly different voltage ratios or impedances, which can result in uneven load sharing. Therefore, a method called "circulating current method" is used to balance the load among the transformers. In this method, the transformers are connected in parallel with a set of three-phase busbars, which are used to measure the voltage and current of each transformer. The transformer with the highest voltage is designated as the "master" transformer, and its voltage is used as the reference for the other transformers. The voltage of each transformer is adjusted using tap changers until they match the master voltage. Once the voltages are balanced, the load sharing is determined by measuring the currents of each transformer. If the currents are not balanced, a circulating current will flow between the transformers, which can cause overheating and damage. To eliminate the circulating current, a compensating winding or an autotransformer can be added to each transformer. During operation, the parallel transformers should be regularly inspected and maintained to ensure proper performance and prevent failure. The insulation resistance, oil level, and cooling system should be checked regularly. Any abnormalities or defects should be repaired or replaced immediately.

Explanation: Please refer to solution in this step.

Three-Phase Transformer Parallel Operation of Transformer Content of the Research: Minimum of 5 pages 1. Background (Definition, History, etc) 2. Design 3. Calculation (5 examples) 4. Operation

Public Answer

Three-Phase Transformer

Parallel Operation of Transformer

Content of the Research: Minimum of 5 pages

1. Background (Definition, History, etc)

2. Design

3. Calculation (5 examples)

4. Operation