Name: power triangle in ac circuits
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 14 s
Channel: JoVE

AC電源に接続された負荷について考えてみます。この負荷の両端の電圧と電流は、周波数領域で表すことができます。
複素電力は、電圧と電流の複素共役の半分の積として定義されます。
複素電力の大きさは、皮相電力として知られています。
複素電力を長方形で表す場合、実数部は平均電力を表し、虚数部は無効電力を表します。
複素電力は、電圧と電流の比率であるインピーダンスで表すこともできます。
インピーダンスの抵抗部分とリアクタンス部分を分離し、これらを得られた複素電力式と比較すると、インピーダンスを含む式が得られます。
電力の実際の部分は、負荷に供給される唯一の有用な電力です。
無効電力は、電源と負荷の間のエネルギー交換を反映しています。抵抗性の場合はゼロ、容量性の場合は負、誘導性負荷の場合は正です。
複素電力、実電力、無効電力は、パワートライアングルと呼ばれる三角形の形で視覚化できます。

複素電力

電気エンジニアは、並列負荷の累積効果を判断するために複素電力の概念を導入しました。この考え方は、特定の負荷によって消費される電力に関連するすべての詳細を網羅しているため、電力分析において重要な役割を果たします。

複素電力は、電圧と電流の複素共役の乗算として定義されます。この電力の大きさは皮相電力と呼ばれ、ボルトアンペア (VA) で測定されます。特に、複素電力の角度は力率角度に相当します。

rms 値では、複素電力は次のように表されます。

<img alt="Equation 1" src="/files/ftp_upload/15120/15120_Equation_1.svg" style="height: 18px;">

負荷インピーダンスでは、次のように表すこともできます。

<img alt="Equation 2" src="/files/ftp_upload/15120/15120_Equation_2.svg" style="height: 20px;">

複素電力は、rms 電圧位相器と rms 電流位相器の複素共役の積です。複素量であるため、実部は実電力 P と呼ばれ、虚部は無効電力 Q と呼ばれます。複素電力の導入により、電圧と電流の位相器から実電力と無効電力を直接取得できるようになり、複素電力が特定の負荷のすべての関連電力情報をどのようにカプセル化しているかが示されます。

無効電力は、ソースと負荷間のエネルギー転送を表します。抵抗負荷の場合はゼロ、容量負荷の場合は負、誘導負荷の場合は正です。

複素電力、実電力、無効電力は、一般に電力三角形と呼ばれる三角形の形で視覚化できます。この視覚化は、これらの電力の概念を理解するのに役立ちます。

AC電源に接続された負荷について考えてみます。この負荷の両端の電圧と電流は、周波数領域で表すことができます。
その複雑な力は...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Steady State Power

交流定常状態電力

KEY TERMS AND CONCEPTS

主要用語と概念

Complex Power

power triangle in ac circuits

Power triangle and complex power help describe how an AC load uses energy. Engineers use complex power to capture the combined effect of parallel loads. It gives a full picture of the power consumed by a specific load.

Complex power is found by multiplying voltage by the complex conjugate of current. Using rms values, it is written with the rms voltage phasor and the complex conjugate of the rms current phasor. It can also be written in terms of load impedance.

The magnitude of complex power is called apparent power. Apparent power is measured in volt-amperes, or VA. The angle of complex power is the same as the power factor angle.

Because complex power is a complex number, its real part is real power P and its imaginary part is reactive power Q. Real and reactive power can be read directly from the voltage and current phasors. This shows how complex power stores all the important power information for a load.

Reactive power describes energy transfer between the source and the load. For resistive loads, reactive power is zero. For capacitive loads, it is negative, and for inductive loads, it is positive.

These power terms are often shown in a triangle called the power triangle. The triangle includes complex power, real power, and reactive power. This visual model makes the relationships between the power quantities easier to understand.

Power Triangle in AC Circuits

instantaneous power

AC Power and Phase Shift

Instantaneous power in an electrical circuit comes from the voltage across an element and the current through it. It is written as p(t) and follows the passive sign convention. For sinusoidal input, this product helps show how power changes at each moment. When instantaneous power is expanded, it has two parts. One part is constant and depends on the phase difference between voltage and current. The other part is a sinusoidal term that varies at twice the frequency of the voltage or current. <br...

average power

Power Consumption in AC Circuits

Power consumption in AC circuits is often described with average power. In practical electrical work, the changing value of instantaneous power is less useful than the average over a time period. Average power is found by integrating instantaneous power over that time and then dividing by the duration. The time-domain expression for average power comes from simplifying the equation for instantaneous power. In that form, one cosine term averages to zero over a complete cycle. The result does...

effective value of a periodic waveform

RMS Value for AC Power Measurement

The RMS value, or effective value, helps measure how much power a periodic voltage or current can deliver. It is the direct current, or DC, value that gives the same average power to a resistor as the periodic signal does. This idea is especially important in AC circuits. To find the effective value of current, calculate the root mean square, or RMS, current. First square the instantaneous current values over one period. Then find the mean of those squared values and take the square root. The...

complex power

Power triangle and complex power help describe how an AC load uses energy. Engineers use complex power to capture the combined effect of parallel loads. It gives a full picture of the power consumed by a specific load. Complex power is found by multiplying voltage by the complex conjugate of current. Using rms values, it is written with the rms voltage phasor and the complex conjugate of the rms current phasor. It can also be written in terms of load impedance. The magnitude of complex power...

conservation of ac power

AC Power in Series and Parallel Circuits

AC power in series and parallel circuits follows a power preservation rule. In AC circuits, the complex power, real power, and reactive power produced by the source are equal to the total complex, real, and reactive powers absorbed by the loads. When two load impedances are connected in parallel to an AC source V, the source power can be written as the sum of the complex powers delivered to loads Z1 and Z2. If those same loads are connected in series with the voltage source, the complex power...

power factor

Power Factor and AC Load Behavior

Power factor describes how voltage and current behave in an AC load. It is the ratio of average, or active, power to apparent power. The power factor angle is the phase difference between voltage and current, and the cosine of that angle gives the power factor. It also matches the angle of the load impedance. Power factor shows how much apparent power becomes real, or average, power. Its value ranges from zero to one. When a load is purely resistive, voltage and current are in phase. In that...

power factor correction

Reducing Reactive Power in AC Loads

Power factor correction helps AC systems use electrical power more efficiently. In a factory circuit, transmitted power includes apparent power, which is made of active power and reactive power. Power factor is the ratio of real power, measured in kW, to apparent power, measured in kVA. It shows how much of the supplied power becomes useful work. A low power factor often happens when an inductive load draws too much reactive power. This creates a lagging power factor. It can also cause large...

the power superposition principle

Power from Multiple AC Sources

Power from multiple AC sources is found by adding the effects of each source separately. In a circuit with two sinusoidal voltage sources, each source acts independently. The superposition principle says the total current is the sum of the currents produced by each source alone. If those currents are labeled i1 and i2, they combine to give the total current. Instantaneous power is the power at one moment in time. In this circuit, it equals the square of the instantaneous current times the...

the maximum power transfer theorem

Matching Load Impedance for Maximum Power

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form. The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated...

key terms and concepts

Learn how complex power, apparent power, real power, and reactive power are related in AC circuits, and how the power triangle helps explain them.

Power Triangle in AC Circuits | 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

Power Triangle in AC Circuits

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