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

In Stromnetzen verfügen symmetrische Y-zu-Delta-Schaltungen über Y-verbundene Spannungsquellen und Delta-verbundene Lasten, in der Regel ohne Neutralleiter.
Unter der Annahme einer positiven Phasenfolge werden die Phasenspannungen ausgedrückt, um die Netzspannungen zu schätzen.
Diese Netzspannungen entsprechen den Spannungen über die Lastimpedanzen und erleichtern die Berechnung von Phasenströmen, die ähnliche Größenordnungen haben und um 120 Grad phasenverschoben sind.
Die Anwendung des Kirchhoffschen Stromgesetzes an den Knoten der delta-verbundenen Verbraucher zeigt den Zusammenhang zwischen dem Linien- und dem Phasenstrom.
Die Größen der berechneten Linienströme sind die Quadratwurzel des Dreifachen der Größen der entsprechenden Phasenströme, und die Linienströme hinken den Phasenströmen um 30 Grad hinterher.
Eine weitere Möglichkeit, das Y-zu-Delta-System zu analysieren, besteht darin, die mit Delta verbundenen Verbraucher in die entsprechende Y-Konfiguration umzuwandeln.
Das resultierende symmetrische Y-zu-Y-System kann dann analysiert werden, indem seine einphasige Ersatzschaltung berücksichtigt und die Netzströme bestimmt werden.
Die Größen und Phasenwinkel der Phasenströme werden aus den entsprechenden Linienströmen mit Hilfe geeigneter Delta-zu-Y-Transformationen berechnet.

der stern-dreieck-schaltkreis

Ein symmetrischer Stern-Dreieck-Schaltkreis besteht aus symmetrischen, sternförmig angeschlossenen Spannungsquellen und dreieckförmig angeschlossenen Lasten ohne Neutralleiteranschluss.

Der erste Schritt bei der Analyse eines Stern-Dreieck-Schaltkreises besteht darin, eine positive Phasenfolge anzunehmen. Diese Phasenspannungen werden dann verwendet, um die Leitungsspannungen zu berechnen, die direkt über den dreieckförmig angeschlossenen Lastimpedanzen auftreten. V_an, V_bn und V_cn sind die Phasenspannungen im Stern, und V_ab, V_bc und V_ca sind die Leitungsspannungen für einen Dreieck-Schaltkreis. Die Beziehung zwischen den Leitungsspannungen für einen Stern-Dreieck-Schaltkreis kann wie folgt berechnet werden:

<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_1.svg" style="text-align: center; height: 13px;">

<img alt="Equation 2" src="/files/ftp_upload/15130/15130_Equation_2.svg" style="text-align: center; height: 13px;">

<img alt="Equation 3" src="/files/ftp_upload/15130/15130_Equation_3.svg" style="text-align: center; height: 13px;">

Diese Spannungen über den Lastimpedanzen werden anschließend verwendet, um die Phasenströme nach dem Ohmschen Gesetz zu berechnen. Aufgrund der symmetrischen Natur des Schaltkreises haben diese Phasenströme identische Größen, sind aber in der Phase um 120 Grad getrennt.

Das Kirchhoffsche Stromgesetz (KCL) wird an den Knotenpunkten der im Dreieck angeschlossenen Lasten angewendet, um die Beziehung zwischen Leitungs- und Phasenströmen abzuleiten.

In einem symmetrischen Stern-Dreieck-System ist die Größe der Leitungsströme mit der Größe der Phasenströme um einen Faktor der Quadratwurzel aus 3 verknüpft. Die Leitungsströme hinken ihren entsprechenden Phasenströmen in der Dreieckkonfiguration um 30 Grad hinterher.

Eine alternative Methode zur Analyse des Stern-Dreieck-Schaltkreises besteht darin, die in Dreieckschaltung angeschlossenen Lasten in eine äquivalente Sternschaltung umzuwandeln. Dadurch wird der Schaltkreis in ein ausgeglichenes Stern-Dreieck-System umgewandelt, das zur Analyse in einphasige äquivalente Schaltkreise vereinfacht werden kann. Auf diese Weise können die Phasenströme aus ihren entsprechenden Leitungsströmen geschätzt werden, wobei die durch die Umwandlung verursachte Phasenverschiebung berücksichtigt wird.

Dieses detaillierte Verständnis der Phasen- und Leitungsströme und der Beziehung zwischen in Sternschaltung angeschlossenen Quellen und in Dreieckschaltung angeschlossenen Lasten ist für die Entwicklung und den Betrieb eines effizienten elektrischen Systems von entscheidender Bedeutung.

Der Stern-Dreieck-Schaltkreis

In Stromnetzen verfügen symmetrische Y-zu-Delta-Schaltungen über Y-verbundene Spannungsquellen und Delta-verbundene Lasten, in der Regel ohne Neutralleiter.
...

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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

How Three-Phase Power Delivers Electricity

Three-phase power is a major part of AC power distribution, especially where steady and efficient electricity delivery is needed. AC systems are grouped into single-phase, two-phase, and three-phase systems. These categories help describe how power moves from the source to the load. Single-phase circuits are common in homes. They usually use a two-wire system that connects one AC source to loads. These circuits can supply everyday appliances such as lamps, televisions, and microwaves at 120 V...

generation of three-phase voltage

Three-Phase AC Generator Windings

A three-phase AC generator uses rotating magnet windings and a stationary stator to make three-phase voltage. The rotor carries a magnet that spins inside the stator. The stator holds the three-phase winding, and mutual induction creates the voltage. The stator windings are spread evenly around the inside of the stator. They are placed 120 electrical degrees apart. These windings consist of three separate coils, or groups of coils, called phases. The phases can be connected in a Y, or star,...

three-phase voltages

Three-Phase Power Connections

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...

power distribution in three-phase and single phase circuits

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

Single-Phase vs. Three-Phase Power Loss

Single-phase and three-phase circuits distribute electrical power in different ways. Single-phase power is common in homes, while balanced three-phase power is widely used in industrial settings with heavy machinery. Both systems deliver energy, but their current flow and wire needs are not the same. A single-phase circuit usually uses a two-wire system. The current depends on the power absorbed by the load and the line voltage. Because wire loss from resistance follows the square of the...

line loss

Reducing Power Loss in Three-Phase Lines

Three-phase power lines can lose energy as electricity travels from the source to the load. This line loss affects how efficiently power reaches the load. In balanced three-phase circuits, the symmetry makes the analysis easier because one phase can represent the whole system. The source-load connection can use wye, also called star, or delta configurations. These setups change the relationship between line voltage, phase voltage, line current, and phase current. A per-phase equivalent circuit...

reducing line loss

Cutting Heat Loss in Three-Phase Lines

Three-phase power systems can lose energy as heat in transmission lines because the wires have resistance. This line loss becomes important when electricity travels over a distance. A common solution is to use transformers to change the voltage and current in the system. The setup uses two three-phase transformers. A step-up transformer is placed at the source, and a step-down transformer is placed at the load. Raising the voltage at the source lowers the current in the transmission lines, and...

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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