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

Dans les réseaux électriques, les circuits équilibrés Y-Delta-Delta comportent des sources de tension connectées en Y et des charges connectées en Delta, généralement sans ligne neutre.
En supposant une séquence de phases positives, les tensions de phase sont exprimées pour estimer les tensions de ligne.
Ces tensions de ligne sont égales aux tensions aux bornes des impédances de charge et facilitent le calcul des courants de phase, qui ont des amplitudes similaires et sont déphasés de 120 degrés.
L'application de la loi de courant de Kirchhoff aux nœuds des charges connectées en delta révèle la relation entre les courants de ligne et de phase.
Les amplitudes des courants de ligne calculés sont la racine carrée de trois fois les intensités des courants de phase correspondants, et les courants de ligne sont en retard de 30 degrés sur les courants de phase.
Une autre façon d’analyser le système Y-à Delta consiste à convertir les charges connectées en delta dans leur configuration Y correspondante.
Le système équilibré d’Y à Y résultant peut ensuite être analysé en considérant son circuit équivalent monophasé et en déterminant les courants de ligne.
Les amplitudes et les angles de phase des courants de phase sont calculés à partir de leurs courants de ligne correspondants à l’aide de transformations Delta-Y appropriées.

le circuit y-vers-delta

Un circuit étoile-triangle équilibré comprend des sources de tension équilibrées connectées en Y et des charges connectées en triangle sans connexion de ligne neutre.

La première étape de l’analyse d’un circuit étoile-triangle consiste à supposer une séquence de phases positive. Ces tensions de phase sont ensuite utilisées pour calculer les tensions de ligne qui se produisent directement aux bornes des impédances de charge connectées en triangle. Van, Vbn, et Vcn sont les tensions de phase en étoile, et Van, Vbn, et Vcn sont les tensions de ligne pour un circuit en triangle. La relation entre les tensions de ligne pour un circuit étoile-triangle peut être calculée comme suit :

<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_1.svg" style="text-align: center; height: 13px;">

<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_2.svg" style="text-align: center; height: 13px;">

<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_3.svg" style="text-align: center; height: 13px;">

Ces tensions aux bornes des impédances de charge sont ensuite utilisées pour calculer les courants de phase à l'aide de la loi d'Ohm. En raison de la nature équilibrée du circuit, ces courants de phase ont des amplitudes identiques mais sont séparés en phase de 120 degrés.

La loi des courants de Kirchhoff (KCL) est appliquée aux nœuds des charges connectées en triangle pour dériver la relation entre les courants de ligne et de phase.

Dans un système étoile-triangle équilibré, l'amplitude des courants de ligne est liée à l'amplitude des courants de phase par un facteur de racine carrée de 3. Les courants de ligne sont en retard de 30 degrés par rapport à leurs courants de phase correspondants dans la configuration en triangle.

Une autre méthode d’analyse du circuit étoile-triangle consiste à transformer les charges connectées en triangle en une configuration en étoile équivalente. Cela convertira le circuit en un système étoile-étoile équilibré, qui peut être simplifié en circuits équivalents monophasés pour l'analyse. De cette manière, les courants de phase peuvent être estimés à partir de leurs courants de ligne correspondants, en tenant compte du déphasage introduit par la transformation.

Cette compréhension détaillée des courants de phase et de ligne et de la relation entre les sources connectées en étoile et les charges connectées en triangle est essentielle pour concevoir et exploiter un système électrique efficace.

le circuit Y-vers-Delta

Dans les réseaux électriques, les circuits équilibrés Y-Delta-Delta comportent des sources de tension connectées en Y et des charges connectées en Delta, généralement sans ligne neutre.
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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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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.

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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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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.

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Wye Source and Delta Load Currents

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