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

En las redes de energía eléctrica, los circuitos balanceados de Y a triángulo cuentan con fuentes de voltaje conectadas a Y y cargas conectadas en triángulo, generalmente sin una línea neutra.
Suponiendo una secuencia de fase positiva, los voltajes de fase se expresan para estimar los voltajes de línea.
Estos voltajes de línea son iguales a los voltajes a través de las impedancias de carga y facilitan el cálculo de corrientes de fase, que tienen magnitudes similares y están desfasadas en 120 grados.
La aplicación de la ley de corriente de Kirchhoff en los nodos de las cargas conectadas en delta revela la relación entre las corrientes de línea y de fase.
Las magnitudes de las corrientes de línea calculadas son la raíz cuadrada de tres veces las magnitudes de las corrientes de fase correspondientes, y las corrientes de línea se retrasan 30 grados con respecto a las corrientes de fase.
Otra forma de analizar el sistema Y-a-Delta es convertir las cargas conectadas en delta a su configuración Y correspondiente.
El sistema Y-a-Y equilibrado resultante se puede analizar considerando su circuito equivalente monofásico y determinando las corrientes de línea.
Las magnitudes y los ángulos de fase de las corrientes de fase se calculan a partir de sus correspondientes corrientes de línea utilizando las transformaciones de Delta a Y adecuadas.

el circuito y-a-Δ

Un circuito equilibrado estrella a triángulo comprende fuentes de voltaje equilibradas conectadas en Estrella y cargas conectadas en triángulo sin conexión de línea neutra.
El paso inicial para analizar un circuito estrella a triángulo es asumir una secuencia de fases positiva. Estos voltajes de fase se utilizan luego para calcular los voltajes de línea que ocurren directamente a través de las impedancias de carga conectadas en triángulo. V_an, V_bn y V_cn son los voltajes de fase en estrella, y V_ab, V_bc y V_ca son los voltajes de línea para un circuito en triángulo. La relación entre los voltajes de línea para un circuito estrella a triángulo se puede calcular 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;">
Estos voltajes a través de las impedancias de carga se utilizan posteriormente para calcular las corrientes de fase utilizando la ley de Ohm. Debido a la naturaleza equilibrada del circuito, estas corrientes de fase tienen magnitudes idénticas pero están separadas en fase por 120 grados.
La Ley de Corrientes de Kirchhoff (KCL) se aplica en los nodos de las cargas conectadas en triángulo para derivar la relación entre las corrientes de línea y de fase.
En un sistema equilibrado estrella a triángulo, la magnitud de las corrientes de línea está relacionada con las magnitudes de las corrientes de fase por un factor de raíz cuadrada de 3. Las corrientes de línea están retrasadas 30 grados con respecto a sus corrientes de fase correspondientes en la configuración triángulo.
Un método alternativo para analizar el circuito estrella a triángulo es transformar las cargas conectadas en triángulo a una configuración estrella equivalente. Esto convertirá el circuito en un sistema equilibrado estrella a estrella, que se puede simplificar en circuitos equivalentes monofásicos para su análisis. De esta manera, se pueden estimar las corrientes de fase a partir de sus correspondientes corrientes de línea, considerando el desfase introducido por la transformación.
Esta comprensión detallada de las corrientes de fase y de línea y la relación entre las fuentes conectadas en estrella y las cargas conectadas en triángulo es esencial para diseñar y operar un sistema eléctrico eficiente.

El circuito Y-a-Δ

En las redes de energía eléctrica, los circuitos balanceados de Y a triángulo cuentan con fuentes de voltaje conectadas a Y y cargas conectadas en triángulo, generalmente sin una línea neutra.
...

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Electrical Engineering

Ingeniería Eléctrica

Unit 1

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Three-Phase Circuits

Circuitos trifásicos

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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

three-phase circuits

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Three-phase power connections use balanced voltages that are equal in magnitude and separated by 120 degrees. A three-phase generator produces these voltages, and the balance helps reduce power loss while keeping energy delivery steady to connected loads. Three-phase sources can be arranged in either wye or delta form. The loads connected to the system can also use wye or delta. This flexibility gives control over how the system is designed and managed. In a wye connection, one end of each...

the y-to-y circuit

Balanced Wye-to-Wye Neutral Current

A balanced wye-to-wye circuit uses three wye-connected sinusoidal voltage sources and three wye-connected loads. A neutral wire links the neutral node of the source to the neutral node of the load. The load impedance is connected across each phase of the load. The source and load can be connected in either a four-wire or a three-wire arrangement. A three-phase system is balanced when each phase has the same load. In that case, the current flow and phase angle are uniform across the system. If...

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

Balanced Delta-Delta Power Circuit

A balanced delta-delta power circuit uses a delta-connected source and a delta-connected load. The two deltas form a closed loop that creates three separate phases. In this setup, the phase voltages are the same as the line voltages. If the source is in positive sequence, the phase voltages can be written directly, and no neutral wire is needed. The delta-connected load current is found by dividing the phase voltage by the impedance of each phase. For line current, Kirchhoff’s Current Law...

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.

power in a three-phase circuit

Balanced Three-Phase Power Calculation

Balanced three-phase power calculation depends on the wye and delta connections used in the circuit. A wye, or star, configuration can use three wires or four wires. A delta configuration connects the components in a closed loop. These connection types change how voltages and currents are arranged, but both are used in three-phase systems. In a balanced three-phase system, instantaneous power is the power at one exact moment. Even though the power in each phase changes over time, the total...

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power-distribution-in-three-phase-and-single-phase-circuits

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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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