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

電力網では、平衡型Y-デルタ回路は、Y接続の電圧源とデルタ接続の負荷を特徴としており、通常は中性線がありません。
正の位相シーケンスを仮定すると、線間電圧を推定するために位相電圧が表されます。
これらのライン電圧は、負荷インピーダンスの両端の電圧と等しく、同程度の大きさで位相が120度ずれている位相電流の計算を容易にします。
デルタ接続された負荷のノードにキルヒホッフの電流法則を適用すると、ライン電流と相電流の関係が明らかになります。
計算されたライン電流の大きさは、対応する相電流の大きさの3倍の平方根であり、ライン電流は相電流より30度遅れます。
Y-to-Deltaシステムを解析する別の方法は、デルタ接続された負荷を対応するY-configurationに変換することです。
結果として得られる平衡Y/Yシステムは、その単相等価回路を考慮し、ライン電流を決定することによって分析できます。
相電流の大きさと位相角は、適切なデルタからYへの変換を使用して、対応するライン電流から計算されます。

y-Δ回路

バランスのとれた Y--Δ回路は、バランスのとれた Y 接続の電圧源と、中性線接続のないデルタ結線の負荷で構成されます。

Y-デルタ回路を解析する最初のステップは、正の位相シーケンスを想定することです。次に、これらの位相電圧を使用して、デルタ結線の負荷インピーダンスの両端で直接発生する線間電圧を計算します。V_an、V_bn、および V_cn は Y の位相電圧であり、V_ab、V_bc、および Vca はデルタ回路の線間電圧です。 Y 型からデルタ型への回路の線間電圧の関係は、次のように計算できます。

<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;">

負荷インピーダンス間のこれらの電圧は、その後、オームの法則を使用して相電流を計算するために使用されます。回路のバランスの性質により、これらの相電流は同じ大きさですが、位相が 120 度離れています。
デルタ接続された負荷のノードにキルヒホッフの電流法則 (KCL) を適用して、線電流と相電流の関係を導き出します。
バランスの取れた Y 型からデルタ型へのシステムでは、線電流の大きさは、相電流の大きさと 3 の平方根の係数で関連しています。線電流は、デルタ構成の対応する相電流から 30 度遅れます。
Y 型からデルタ型への回路を解析する別の方法の 1 つは、デルタ接続された負荷を同等の Y 型構成に変換することです。これにより、回路はバランスの取れた Y 型から Y 型へシステム変換され、解析用に単相の同等回路に簡略化できます。このようにして、変換によって生じる位相シフトを考慮して、対応する線電流から相電流を推定できます。
相電流と線電流、および Y 型接続された電源とデルタ接続された負荷の関係を詳細に理解することは、効率的な電気システムを設計および運用するために不可欠です。

Y-Δ回路

電力網では、平衡型Y-デルタ回路は、Y接続の電圧源とデルタ接続の負荷を特徴としており、通常は中性線がありません。
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Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Three-Phase Circuits

三相回路

KEY TERMS AND CONCEPTS

主要用語および概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Wye Source and Delta Load Currents

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