Name: power factor and ac load behavior
Uploaded: 2024-07-08T13:19:54.000Z
Duration: 1 min 11 s
Channel: JoVE

力率は、皮相電力に対する有効電力の比率です。
これは、回路内の無効要素の存在によって生じる電圧と電流の位相差によって決まります。
コーヒーは有用な有効電力を象徴し、泡は無効電力を表し、実際の作業を行っていないにもかかわらず、特定の電化製品で利用されるというアナロジーを描くことができます。
費用はガラス全体をカバーしています。最大値を得るには、無効電力を減らして力率を1に近づける必要があります。
純粋な抵抗性負荷の場合、同相の電圧と電流は、皮相電力がアクティブ電力に等しい単一力率をもたらします。
純粋に無効負荷の場合、力率はゼロであり、有効電力がゼロであることを意味します。
これらの両極端の間で、力率は先行または遅れています。先行力率は、電流が電圧をリードしていることを示し、容量性負荷を意味します。
力率の遅れは、電流が電圧より遅れていることを意味し、誘導性負荷を示します。

力率

力率は、平均 (または有効) 電力と皮相電力の比として定義され、次の関係で示されます。

<img alt="Equation 1" src="/files/ftp_upload/15122/15122_Equation_1.svg" style="height: 30px;">

括弧内の項 (θ_v - θ_i) は、力率角と呼ばれます。 これは、余弦が力率を生み出す角度を表すためです。V が負荷の両端の電圧を表し、I が負荷を流れる電流を表す場合、力率角は負荷インピーダンスの角度に等しくなります。基本的に、力率は、電圧と電流の位相差の余弦と、負荷インピーダンスの角度の余弦です。

上記の式から、力率は皮相電力が実電力または平均電力を生み出すための乗数であると推測できます。力率の値は 0 から 1 の範囲です。純粋に抵抗性の負荷を扱う場合、電圧と電流は同位相であるため、力率角 (θ_v - θ_i) = 0、力率 = 1 となります。これは、皮相電力が平均電力に等しいことを示しています。 純粋に無効電力の負荷の場合、(θ_v - θ_i) = ±90o、力率 = 0 となり、電力はゼロになります。この 2 つの極端な状態の間で、 力率は進み力率または遅れ力率のいずれかであると言われています。進み力率は、電流が電圧に先行することを示し、容量性負荷を示します。一方、遅れ力率は、電流が電圧に追従していることを示し、誘導性負荷を示します。力率は、消費者が電力会社に支払う電気料金に大きな影響を与えます。

力率は、皮相電力に対する有効電力の比率です。
これは、電圧と電流の位相差によって決まります。

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

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 case, the power factor angle is 0 and the power factor is 1, so apparent power equals average power.

A purely reactive load gives the opposite extreme. The phase difference is ±90°, and the power factor is 0, so the power is zero. Between these limits, the power factor can be leading or lagging. A leading power factor means current leads voltage, which points to a capacitive load. A lagging power factor means current follows voltage, which points to an inductive load.

Power factor also matters in everyday electricity use. It affects the electricity bills customers pay to utility companies. Understanding it helps explain why the phase relationship between voltage and current is important in AC circuits.

Power Factor and AC Load Behavior

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 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...

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 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 power factor links voltage, current, and AC load behavior. Explore phase difference, leading and lagging loads, and why it affects electricity bills.

Power Factor and AC Load Behavior | 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 Factor and AC Load Behavior

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