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

In electrical power grids, balanced Y-to-Delta circuits feature Y-connected voltage sources and delta-connected loads, typically without a neutral line.
Assuming a positive phase sequence, the phase voltages are expressed to estimate the line voltages.
These line voltages equal the voltages across the load impedances and facilitate the calculation of phase currents, which have similar magnitudes and are out of phase by 120 degrees.
Applying Kirchhoff&#39;s Current Law at the nodes of the delta-connected loads reveals the relationship between the line and phase currents.
The magnitudes of the calculated line currents are the square root of three times the magnitudes of the corresponding phase currents, and the line currents lag the phase currents by 30 degrees.
Another way of analyzing the Y-to-Delta system is to convert the delta-connected loads to their corresponding Y-configuration.
The resulting balanced Y-to-Y system can then be analyzed by considering its single-phase equivalent circuit and determining the line currents.
The magnitudes and phase angles of the phase currents are calculated from their corresponding line currents using appropriate Delta-to-Y transformations.

het y-naar-delta-circuit

Een gebalanceerd Y-naar-Delta-circuit bestaat uit gebalanceerde Y-aangesloten spanningsbronnen en delta-aangesloten belastingen zonder neutrale lijnverbinding.
De eerste stap bij het analyseren van een Y-naar-Delta-circuit is het aannemen van een positieve fasevolgorde. Deze fasespanningen worden vervolgens gebruikt om de lijnspanningen te berekenen die direct over de delta-verbonden belastingsimpedanties optreden. V_an, V_bn en V_cn zijn de fasespanningen in y, en V_ab, V_bc en V_ca zijn de lijnspanningen voor een deltacircuit. De relatie tussen de lijnspanningen voor een Y-naar-Delta-circuit kan als volgt worden berekend:
<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;">

Deze spanningen over de belastingsimpedanties worden vervolgens gebruikt om de fasestromen te berekenen met behulp van de wet van Ohm. Vanwege de gebalanceerde aard van het circuit hebben deze fasestromen dezelfde grootte, maar zijn ze in fase 120 graden gescheiden.
De huidige wet van Kirchhoff (KCL) wordt toegepast op de knooppunten van de delta-verbonden belastingen om de relatie tussen lijn- en fasestromen af te leiden.
In een gebalanceerd y-naar-delta-systeem is de grootte van de lijnstromen gerelateerd aan de grootte van de fasestromen met een factor van de vierkantswortel van 3. Lijnstromen lopen 30 graden achter op hun overeenkomstige fasestromen in de deltaconfiguratie.
Een alternatieve methode voor het analyseren van het Y-naar-Delta-circuit is het transformeren van de delta-verbonden belastingen naar een equivalente Y-configuratie. Hierdoor wordt het circuit omgezet in een gebalanceerd y-to-y-systeem, dat voor analyse kan worden vereenvoudigd tot eenfasige equivalente circuits. Op deze manier kunnen de fasestromen worden geschat op basis van hun overeenkomstige lijnstromen, rekening houdend met de faseverschuiving die door de transformatie wordt geïntroduceerd.
Dit gedetailleerde begrip van fase- en lijnstromen en de relatie tussen Y-verbonden bronnen en delta-verbonden belastingen is essentieel voor het ontwerpen en exploiteren van een efficiënt elektrisch systeem.

Het Y-naar-Delta-circuit

In electrical power grids, balanced Y-to-Delta circuits feature Y-connected voltage sources and delta-connected loads, typically without a neutral line.
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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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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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