Name: balanced three-phase power calculation
Uploaded: 2024-07-08T13:19:58.000Z
Duration: 1 min 15 s
Channel: JoVE

複数の重機を備えた製造工場では、バランスの取れた三相システムによって供給される大量の電力が必要です。
プラントの負荷によって吸収される瞬間的な電力を決定するために、解析はY接続された時間領域回路で実行されます。
相電圧の位相差は120度で、2の平方根を使用してピーク電圧をRMS値に変換し、正確な電力解析を行います。
機械が動作すると、電源から電流が引き出されるため、相電流とそれに対応する相電圧との間に位相遅延が生じます。
機械の負荷によって引き出される総瞬時電力は、3つのフェーズのそれぞれの瞬間電力を合計することによって計算されます。
得られる総瞬時電力はほぼ一定に保たれ、時間とともに変化しません。これにより、フェーズごとの有効電力、無効電力、および皮相電力を計算できます。
総有効電力は、3つのフェーズの有効電力の合計です。同様に、無効電力と皮相電力の合計が計算されます。
これらの結果は、Y接続負荷とデルタ接続負荷の両方に当てはまります。

三相回路の電力

三相システムには、Y 型とΔ型の 2 つの構成があります。スター結線は 3 本または 4 本のワイヤで構成され、デルタ結線ではコンポーネントが閉ループで接続されます。瞬時電力とは、正確な瞬間の電力値を指し、バランスのとれた三相システムでは一定です。これは、対称性と位相関係により、三相の瞬時電力の合計が個々の変動にもかかわらず、時間の経過とともに安定しているためです。バランスのとれた三相システムの合計瞬時電力は一定であり、時間の経過とともに変動しません。
有効電力、無効電力、複合電力:
バランスのとれた三相システムでは、相あたりの平均電力は、平均電力全体の 3 分の 1 です。同様に、相あたりの無効電力は、システム内の無効電力全体の 3 分の 1 です。相あたりの有効電力と無効電力の両方を組み合わせた複合電力も、複合電力全体の 3 分の 1 です。
電力計算における等価性:
デルタおよび Y結線では、すべての相とラインに電圧と電流があります。これらの構成では、負荷は負荷端で各相に接続されます。負荷によって消費される電力と、Y 構成とデルタ構成の等価性は、電力計算にも適用されます。Y 接続システムでもデルタ接続システムでも、総電力は 3 つの相の電力の合計です。これは、ラインと相の電圧と電流の関係を使用して計算できます。Y 接続システムとデルタ接続システムの場合:

<img alt="Equation 1" src="/files/ftp_upload/15133/15133_Equation_1.svg" style="height: 16px;">

複数の重機を備えた製造工場では、バランスの取れた三相システムによって供給される大量の電力が必要です。
瞬間的...

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

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 instantaneous power stays constant. The three phase powers add together in a steady way because the system is symmetric and the phases are shifted from one another.

The same one-third relationship applies to average power, reactive power, and complex power. The average power in each phase is one-third of the total average power. The reactive power per phase is also one-third of the total reactive power. Complex power, which combines active and reactive power for each phase, is likewise one-third of the total complex power.

These power rules apply to both wye-connected and delta-connected loads. In both configurations, the load is connected to each phase at the load end. The total power is the sum of the power in the three phases. It can be found by using the known relationships between line voltage, phase voltage, line current, and phase current in either a wye or delta system.

Balanced Three-Phase Power Calculation

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

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 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 three-phase systems handle instantaneous, active, reactive, and complex power in wye and delta connections for high school physics.

Balanced Three-Phase Power Calculation | 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

Balanced Three-Phase Power Calculation

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