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

Ein ausgeglichenes Delta-zu-Delta-System verfügt über eine mit Delta verbundene Quelle und Last.
Es wird davon ausgegangen, dass die mit Delta verbundenen Quellen in positiver Reihenfolge sind, um die Phasenspannungen auszudrücken, die mit den Netzspannungen identisch sind.
Unter der Annahme einer Leitungsimpedanz von Null stimmen die Phasenspannungen mit der Spannung über die Impedanzen überein.
Die Phasenströme entsprechen dem Verhältnis von Phasenspannung und Lastimpedanz pro Phase.
Netzströme werden aus Phasenströmen unter Verwendung des Kirchhoffschen Stromgesetzes an Knoten der delta verbundenen Verbraucher abgeleitet.
Jeder Linienstrom hinkt seinem entsprechenden Phasenstrom um 30 Grad hinterher, wobei seine Größe die Quadratwurzel des Dreifachen des Phasenstroms ist.
Alternativ kann die Delta-zu-Delta-Schaltung analysiert werden, indem die Quelle und die Last in ihre Y-Äquivalente konvertiert werden.
Für die mit Y verbundene Quelle entspricht die entsprechende Phasenspannung jeder Netzspannung der mit Delta verbundenen Quelle geteilt durch eine Quadratwurzel aus drei, und ihre Phase wird um minus 30 Grad verschoben.
Die Y-verbundene Lastimpedanz entspricht der Delta-verbundenen Lastimpedanz geteilt durch drei.
Nun kann die äquivalente einphasige Schaltung zur Bestimmung der drei Netzströme verwendet werden.

der delta-zu-delta-schaltkreis

In einer Delta-Delta-Konfiguration sind Quelle und Last in einer Delta-Konfiguration verbunden und bilden eine geschlossene Schleife, die das Netzwerk in drei verschiedene Phasen aufteilt. Diese Konfiguration macht die Phasenspannungen identisch mit den Leitungsspannungen. Unter der Annahme, dass die Quellen in positiver Sequenz sind, können die Phasenspannungen direkt ausgedrückt werden, ohne dass ein Neutralleiter vorhanden ist.

<img alt="Equation 1" src="/files/ftp_upload/15131/15131_Equation_1.svg" style="text-align: center; height: 13px;">

Die Phasenströme in einer Delta-verbundenen Last werden berechnet, indem die Phasenspannung durch die Lastimpedanz pro Phase geteilt wird:

<img alt="Equation 2" src="/files/ftp_upload/15131/15131_Equation_2.svg" style="text-align: center; height: 32px;">

In dieser Konfiguration gibt Kirchhoffs Stromgesetz (KCL) jeden Leitungsstrom als Vektorsumme der Ströme der verbleibenden zwei Phasen an, was zu dem allgemeinen Prinzip führt, dass jeder Leitungsstrom die Quadratwurzel aus dem Dreifachen der Stärke des Phasenstroms ist. Er hinkt dem Phasenstrom aufgrund der durch die Delta-Verbindung erzeugten Phasenunterschiede um 30 Grad hinterher.

Die Analyse solcher Systeme umfasst die Umwandlung von Quelle und Last in ihre Stern-Äquivalente. Diese Umwandlung vereinfacht das Dreiphasensystem zu einem einphasigen Äquivalentschaltkreis. Die Umwandlung umfasst die Anpassung von Größe und Phase der Leitungsspannungen der im Dreieck geschalteten Quelle:

<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;">

Außerdem beträgt die Impedanz jeder im Stern geschalteten Last ein Drittel der Impedanz der im Dreieck geschalteten Last.

Ausgeglichene Dreieck-Dreieck-Konfigurationen werden in industriellen Anwendungen für Hochleistungsmaschinen, Transformatoren und Motorsteuerungszentren verwendet. Sie ermöglichen eine effiziente Stromübertragung über lange Distanzen, reduzieren harmonische Verzerrungen und erleichtern den reibungslosen Betrieb von Dreiphasenmotoren, indem sie konstante Spannungspegel aufrechterhalten, ohne dass eine Neutralleiterverbindung erforderlich ist.

Der Delta-zu-Delta-Schaltkreis

Ein ausgeglichenes Delta-zu-Delta-System verfügt über eine mit Delta verbundene Quelle und Last.
Es wird davon ausgegangen, dass die delta-verbundenen Quellen in positiver Reihenfolge sind, um die ...

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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 (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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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

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

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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

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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