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

Сбалансированная система «треугольник-треугольник» имеет источник и нагрузку, подключенные к треугольнику.
Предполагается, что источники, подключенные треугольником, находятся в положительной последовательности для выражения фазных напряжений, которые идентичны сетевым напряжениям.
При условии нулевого линейного сопротивления фазные напряжения соответствуют напряжению на всех импедансах.
Фазные токи равны отношению фазного напряжения и импеданса нагрузки для каждой фазы.
Линейные токи выводятся из фазных токов с использованием закона тока Кирхгофа в узлах напряжений, соединенных треугольником.
Каждый линейный ток отстает от соответствующего фазного тока на 30 градусов, при этом его величина равна квадратному корню из трехкратного фазного тока.
В качестве альтернативы можно проанализировать дельта-дельту цепь путем преобразования источника и нагрузки в их Y-эквиваленты.
Для источника, подключенного по оси Y, соответствующее фазное напряжение равно каждому линейному напряжению источника, подключенного к треугольнику, деленному на квадратный корень из трех, и его фаза смещается на отрицательные 30 градусов.
Импеданс нагрузки, подключенной по оси Y, равен импедансу дельта-соединенной нагрузки, деленному на три.
Теперь для определения трех линейных токов можно использовать эквивалентную однофазную цепь.

Схема «треугольник-треугольник»

The Delta-to-Delta Circuit

В конфигурации «треугольник-треугольник» источник и нагрузка соединяются по схеме «треугольник», образуя замкнутый контур, который делит сеть на три отдельные фазы. Эта конфигурация делает фазные напряжения идентичными линейным напряжениям. Предполагая, что источники расположены в прямой последовательности, фазные напряжения могут быть выражены напрямую, без нейтрального провода.
<img alt="Equation 1" src="/files/ftp_upload/15131/15131_Equation_1.svg" style="height: 13px;">
Фазные токи в нагрузке, соединенной треугольником, рассчитываются путем деления фазного напряжения на полное сопротивление нагрузки на фазу:
<img alt="Equation 2" src="/files/ftp_upload/15131/15131_Equation_2.svg" style="height: 32px;">
В этой конфигурации закон Кирхгофа (KCL) определяет каждый линейный ток как векторную сумму токов оставшихся двух фаз, что приводит к общему принципу, согласно которому каждый линейный ток представляет собой квадратный корень из трех умножить на величину фазного тока. Он отстает от фазного тока на 30 градусов из-за разности фаз, создаваемой соединением треугольником.
Анализ таких систем включает преобразование источника и нагрузки в их звездные эквиваленты. Это преобразование упрощает трехфазную систему в однофазную эквивалентную схему. Преобразование включает в себя регулировку как величины, так и фазы линейного напряжения источника, соединенного треугольником:
<img alt="Equation 3" src="/files/ftp_upload/15131/15131_Equation_3.svg" style="height: 32px;">
<img alt="Equation 4" src="/files/ftp_upload/15131/15131_Equation_4.svg" style="height: 16px;">
Кроме того, импеданс каждой нагрузки, соединенной звездой, составляет одну треть импеданса нагрузки, соединенной треугольником.
Сбалансированные конфигурации «треугольник-треугольник» используются в промышленных приложениях для мощного оборудования, трансформаторов и центров управления двигателями. Они обеспечивают эффективную передачу энергии на большие расстояния, уменьшают гармонические искажения и способствуют плавной работе трехфазных двигателей, поддерживая постоянный уровень напряжения без необходимости подключения нейтрали.

Сбалансированная система «треугольник-треугольник» имеет источник и нагрузку, подключенные к треугольнику.
Предполагается, что источники, подключенные к дельте, находятся в положительной последовательности для выражения ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Three-Phase Circuits

Трехфазные цепи

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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

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...

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

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

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.

electrical engineering

Balanced Delta-Delta Power Circuit

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