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

В электрических сетях сбалансированные цепи Y-to-Delta оснащены источниками напряжения, подключенными по оси Y, и нагрузками, подключенными по треугольнику, как правило, без нейтральной линии.
Предполагая положительную последовательность фаз, фазные напряжения выражаются для оценки напряжения в сети.
Эти линейные напряжения равны напряжениям на импедансах нагрузки и облегчают расчет фазных токов, которые имеют схожие величины и отклоняются по фазе на 120 градусов.
Применение закона тока Кирхгофа к узлам дельта-подключенных нагрузок позволяет выявить взаимосвязь между линейным и фазным токами.
Величины рассчитанных линейных токов равны квадратному корню из трех величин соответствующих фазных токов, а линейные токи отстают от фазных токов на 30 градусов.
Другой способ анализа системы Y-to-Delta заключается в преобразовании нагрузок, подключенных к дельте, в соответствующую Y-конфигурацию.
Полученная сбалансированная система Y-to-Y может быть затем проанализирована путем рассмотрения ее однофазной эквивалентной цепи и определения линейных токов.
Величины и фазовые углы фазных токов рассчитываются на основе соответствующих линейных токов с использованием соответствующих преобразований Delta-to-Y.

Схема y-delta (“звезда” - “треугольник”)

Сбалансированная схема «звезда-треугольник» включает симметричные источники напряжения, соединенные по схеме “звезда”, и нагрузки, соединенные по схеме «треугольник», без подключения к нейтральной линии.
Первым шагом при анализе схемы «звезда-треугольник» является предположение о положительной последовательности фаз. Эти фазные напряжения затем используются для расчета линейных напряжений, которые возникают непосредственно на импедансах нагрузки, соединенных треугольником. V_an, V_bn и V_cn — фазные напряжения в схеме «звезда», а V_ab, V_bc и V_ca — линейные напряжения для схемы треугольника. Соотношение между линейными напряжениями для схемы «звезда-треугольник» можно рассчитать как:
<img alt="Equation 1" src="/files/ftp_upload/15130/15130_Equation_1.svg" style="height: 13px;">
<img alt="Equation 2" src="/files/ftp_upload/15130/15130_Equation_2.svg" style="height: 13px;">
<img alt="Equation 3" src="/files/ftp_upload/15130/15130_Equation_3.svg" style="height: 13px;">
Эти напряжения на импедансах нагрузки впоследствии используются для расчета фазных токов с использованием закона Ома. Из-за сбалансированности схемы эти фазные токи имеют одинаковые величины, но разделены по фазе на 120 градусов.
Закон Кирхгофа по току (KCL) применяется в узлах нагрузок, соединенных треугольником, для определения взаимосвязи между линейными и фазными токами.
В сбалансированной системе «звезда-треугольник» величина линейных токов связана с величинами фазных токов с коэффициентом пропорциональности квадратный корень из 3. Линейные токи отстают на 30 градусов от соответствующих им фазных токов в конфигурации треугольника.
Одним из альтернативных методов анализа схемы «звезда-треугольник» является преобразование подключенных по треугольнику нагрузок в эквивалентную конфигурацию звезды. Это преобразует схему в сбалансированную систему «звезда-звезда», которую для анализа можно упростить до однофазных эквивалентных схем. Таким образом, фазные токи можно оценить по соответствующим линейным токам с учетом фазового сдвига, вносимого преобразованием.
Такое детальное понимание фазовых и линейных токов, а также взаимоотношений между источниками, соединенными звездой, и нагрузками, соединенными треугольником, имеет важное значение для проектирования и эксплуатации эффективной электрической системы.

Схема Y-Delta (“звезда” - “треугольник”)

В электрических сетях сбалансированные цепи Y-to-Delta оснащены источниками напряжения, подключенными по оси Y, и нагрузками, подключенными по треугольнику, как правило, без нейтральной линии.
...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Three-Phase Circuits

Трехфазные цепи

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

Description

Transcript