Name: balanced delta-delta power circuit
Uploaded: 2024-07-08T13:19:57.000Z
Duration: 1 min 17 s
Channel: JoVE

Un système équilibré delta à delta a une source et une charge connectées en delta.
Les sources connectées en triangle sont supposées être en séquence positive pour exprimer les tensions de phase, qui sont identiques aux tensions de ligne.
En supposant des impédances de ligne nulles, les tensions de phase correspondent à la tension aux bornes des impédances.
Les courants de phase sont égaux au rapport entre la tension de phase et l’impédance de charge par phase.
Les courants de ligne sont dérivés des courants de phase à l'aide de la loi de courant de Kirchhoff aux nœuds des charges connectées en delta.
Chaque courant de ligne est en retard de 30 degrés par rapport au courant de phase correspondant, son amplitude étant la racine carrée de trois fois le courant de phase.
Alternativement, le circuit delta à delta peut être analysé en convertissant la source et la charge en leurs équivalents Y.
Pour la source connectée en Y, la tension de phase correspondante est égale à chaque tension de ligne de la source connectée en triangle divisée par une racine carrée de trois, et sa phase est décalée de moins 30 degrés.
L’impédance de charge connectée en Y est égale à l’impédance de charge connectée en delta divisée par trois.
Maintenant, le circuit monophasé équivalent peut être utilisé pour déterminer les trois courants de ligne.

le circuit delta-delta

The Delta-to-Delta Circuit

Dans une configuration delta-delta, la source et la charge sont connectées en triangle, formant une boucle fermée qui divise le réseau en trois phases distinctes. Cette configuration rend les tensions de phase identiques aux tensions de ligne. En supposant que les sources sont en séquence positive, les tensions de phase peuvent être exprimées directement sans avoir de fil neutre. 
<img alt="Equation 1" src="/files/ftp_upload/15131/15131_Equation_1.svg" style="text-align: center; height: 13px;">
Les courants de phase dans une charge connectée en triangle sont calculés en divisant la tension de phase par l'impédance de charge par phase : 
<img alt="Equation 2" src="/files/ftp_upload/15131/15131_Equation_2.svg" style="text-align: center; height: 32px;">
Dans cette configuration, la loi des courants de Kirchhoff (KCL) donne à chaque courant de ligne la somme vectorielle des courants des deux phases restantes, conduisant au principe général selon lequel chaque courant de ligne est la racine carrée de trois fois l'amplitude du courant de phase. Il est en retard de 30 degrés sur le courant de phase en raison des différences de phase créées par la connexion en triangle.
Les analyses de tels systèmes impliquent la conversion de la source et de la charge en leurs équivalents en étoile. Cette conversion simplifie le système triphasé en un circuit équivalent monophasé. La conversion implique d'ajuster à la fois l'amplitude et la phase des tensions de ligne de la source connectée en triangle : 
<img alt="Equation 3" src="/files/ftp_upload/15131/15131_Equation_3.svg" style="text-align: center; height: 32px;">
<img alt="Equation 4" src="/files/ftp_upload/15131/15131_Equation_4.svg" style="text-align: center; height: 16px;">
De plus, l'impédance de chaque charge connectée en étoile est égale au tiers de l'impédance de la charge connectée en triangle.
Les configurations triangle-triangle équilibrées sont utilisées dans les applications industrielles pour les machines, les transformateurs et les centres de contrôle de moteurs de haute puissance. Elles permettent une transmission efficace de l'énergie sur de longues distances, réduisent la distorsion harmonique et facilitent le bon fonctionnement des moteurs triphasés en maintenant des niveaux de tension constants sans avoir besoin d'une connexion neutre.

Le circuit Delta-Delta

Un système équilibré delta à delta a une source et une charge connectées en delta.
On suppose que les sources connectées en delta sont en séquence positive pour exprimer le ...

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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 (KCL) applies at each node. The line current is the vector sum of the currents from the other two phases. In a balanced delta connection, each line current has a magnitude of square root of three times the phase current. It also lags the phase current by 30 degrees because of the phase shift in the delta network.

To analyze the system more simply, the source and load can be changed into wye-equivalents. A wye connection is a star-shaped circuit that makes three-phase analysis easier. This conversion turns the three-phase network into a single-phase equivalent circuit. The delta-connected source voltages must be adjusted in both magnitude and phase during the conversion. The impedance of each wye-connected load is one-third of the delta-connected load impedance.

Balanced delta-delta systems are common in industrial settings. They are used for high-power machines, transformers, and motor control centers. They also support long-distance power transmission and can help reduce harmonic distortion. In three-phase motors, the steady voltage levels help smooth operation without the need for a neutral connection.

Balanced Delta-Delta Power Circuit

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Explore how balanced delta-delta power circuits work, including line and phase voltages, line current, wye-equivalent conversion, and industrial uses.

Balanced Delta-Delta Power Circuit | 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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Balanced Delta-Delta Power Circuit

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