Name: wye source and delta load currents
Uploaded: 2024-07-08T13:19:57.000Z
Duration: 1 min 19 s
Channel: JoVE

Em redes de energia elétrica, os circuitos Y-para-Delta balanceados apresentam fontes de tensão conectadas em Y e cargas conectadas em delta, normalmente sem uma linha neutra.
Assumindo uma sequência de fase positiva, as tensões de fase são expressas para estimar as tensões da linha.
Essas tensões de linha são iguais às tensões nas impedâncias de carga e facilitam o cálculo das correntes de fase, que têm magnitudes semelhantes e estão fora de fase em 120 graus.
A aplicação da Lei da Corrente de Kirchhoff nos nós das cargas conectadas ao delta revela a relação entre a linha e as correntes de fase.
As magnitudes das correntes de linha calculadas são a raiz quadrada de três vezes as magnitudes das correntes de fase correspondentes, e as correntes de linha atrasam as correntes de fase em 30 graus.
Outra maneira de analisar o sistema Y para Delta é converter as cargas conectadas ao delta em sua configuração Y correspondente.
O sistema Y-to-Y balanceado resultante pode então ser analisado considerando seu circuito equivalente monofásico e determinando as correntes de linha.
As magnitudes e ângulos de fase das correntes de fase são calculados a partir de suas correntes de linha correspondentes usando transformações Delta-para-Y apropriadas.

 o circuito y-para-delta

Um circuito estrela-triângulo balanceado compreende fontes de tensão balanceadas conectadas em Y e cargas conectadas em delta sem conexão de linha neutra.

O passo inicial na análise de um circuito estrela-triângulo é assumir uma sequência de fase positiva. Essas tensões de fase são então utilizadas para calcular as tensões de linha que ocorrem diretamente nas impedâncias de carga conectadas em delta. V_an, V_bn e V_cn são as tensões de fase em estrela, e V_ab, V_bc e V_ca são as tensões de linha para um circuito delta. A relação entre as tensões de linha para um circuito estrela-triângulo pode ser calculada como:

<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_1.svg" style="height: 13px;">

<img alt="Equation 2" src="/files/ftp_upload/15130/15130_Equation_2.svg" style="height: 13px;">

<img alt="Equation 3" src="/files/ftp_upload/15130/15130_Equation_3.svg" style="height: 13px;">

Essas tensões nas impedâncias de carga são posteriormente usadas para calcular as correntes de fase usando a lei de Ohm. Devido à natureza equilibrada do circuito, essas correntes de fase têm magnitudes idênticas, mas estão separadas em fase por 120 graus.

A Lei das Correntes de Kirchhoff (KCL) é aplicada nos nós das cargas conectadas em delta para derivar a relação entre as correntes de linha e de fase.

Em um sistema estrela-delta balanceado, a magnitude das correntes de linha está relacionada às magnitudes das correntes de fase por um fator de raiz quadrada de 3. As correntes de linha estão atrasadas 30 graus de suas correntes de fase correspondentes na configuração delta.

Um método alternativo de analisar o circuito estrela-triângulo é transformar as cargas conectadas em delta em uma configuração estrela equivalente. Isso converterá o circuito em um sistema estrela-estrela balanceado, que pode ser simplificado em circuitos equivalentes monofásicos para análise. Desta forma, as correntes de fase podem ser estimadas a partir das correspondentes correntes de linha, considerando o deslocamento de fase introduzido pela transformação.

Esta compreensão detalhada das correntes de fase e linha e da relação entre fontes conectadas em estrela e cargas conectadas em delta é essencial para projetar e operar um sistema elétrico eficiente.

 O circuito Y-para-Delta

Em redes de energia elétrica, os circuitos Y-para-Delta balanceados apresentam fontes de tensão conectadas em Y e cargas conectadas em delta, normalmente sem uma linha neutra.
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Three-Phase Circuits

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KEY TERMS AND CONCEPTS

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The Y-to-Delta Circuit

wye source and delta load currents

A balanced wye source and delta load form a common three-phase circuit with no neutral line connection. The source is Y-connected, and the load is delta-connected. To analyze the circuit, the first step is to assume a positive phase sequence. These phase voltages are then used to find the line voltages that appear across the delta load impedances.

In the wye source, the phase voltages are V an, V bn, and V cn. In the delta load, the line voltages are V ab, V bc, and V ca. These line voltages are the voltages across the load impedances. They are used with Ohm's law to calculate the phase currents in the delta branches.

Because the circuit is balanced, the phase currents all have the same magnitude. They are also separated by 120 degrees. Kirchhoff's Current Law, or KCL, is then applied at the nodes of the delta load to connect line currents and phase currents. In a balanced wye-to-delta system, the line current magnitude is related to the phase current magnitude by a factor of square root of 3.

The line currents also lag their matching phase currents by 30 degrees in the delta configuration. Another way to study the circuit is to transform the delta-connected loads into an equivalent wye. This changes the problem into a balanced wye-to-wye system. That form can be reduced to single-phase equivalent circuits, which makes the current analysis simpler.

Wye Source and Delta Load Currents

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the y-to-delta circuit

A balanced wye source and delta load form a common three-phase circuit with no neutral line connection. The source is Y-connected, and the load is delta-connected. To analyze the circuit, the first step is to assume a positive phase sequence. These phase voltages are then used to find the line voltages that appear across the delta load impedances. In the wye source, the phase voltages are V an, V bn, and V cn. In the delta load, the line voltages are V ab, V bc, and V ca. These line voltages...

the delta-to-delta circuit

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the delta-to-y circuit

Delta-Wye Source and Load Connections

A balanced delta-wye circuit connects a delta-connected source to a wye-connected load. In this setup, the phase voltage of the delta source equals the line voltage of the wye load. The source also sets the line currents that flow into the load. For a balanced system, the phase difference between currents makes it possible to find one line current from the other by using the positive sequence of phases. In the wye-connected load, each phase current equals the line current from the delta source.

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key terms and concepts

Learn how balanced wye sources and delta loads work, including phase voltages, line voltages, KCL, and the 30-degree shift in line currents.

Wye Source and Delta Load Currents | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Wye Source and Delta Load Currents

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