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

功率因数是有功功率与视在功率之比。
它由电压与电流之间的相位差决定，这种相位差源于电路中存在电抗元件。
可以将此情况类比为一杯咖啡，其中咖啡液代表有用的有功功率，而泡沫则代表无功功率——尽管泡沫本身不执行实际做功，但在某些电器设备中会被利用。
成本涵盖整块玻璃。为了实现最大效益，应降低无功功率，使功率因数接近于1。
对于纯电阻负载，电压与电流同相，产生为1的功率因数，此时视在功率等于有功功率。
对于纯电抗性负载，功率因数为零，意味着有功功率为零。
在这两种极端情况之间，功率因数可能为超前或滞后。超前功率因数表示电流超前于电压，说明负载呈电容性。
滞后功率因数表示电流滞后于电压，说明负载为电感性。

功率因数

功率因数能够定义为平均功率（或有功功率）与视在功率之比，其关系式为：

<img alt="Equation 1" src="/files/ftp_upload/15122/15122_Equation_1.svg" style="text-align: center; height: 30px;">

括号中的项 (θ_v - θ_i) 称为功率因数角，因为它表示了余弦中所产生功率因数的角度。如果 V 能够用来表示位于负载两端的电压，Ⅰ能够用来表示流过负载的电流，那么功率因数角就会等于负载阻抗的角度。本质上，功率因数是电压和电流之间相位差的余弦，以及负载阻抗角度的余弦。

从上面的等式可以得知，功率因数是视在功率产生实际功率或平均功率的乘数。功率因数的值通常会介于零和一之间。在处理纯电阻负载时，电压和电流是同相的，从而会导致功率因数角 (θ_v - θ_i) = 0 且功率因数 = 1。这表明了视在功率与平均功率是相等的。对于纯无功负载来说，(θ_v - θ_i) = ±90° 且功率因数 = 0，从而使得功率为零。在这两个极端之间，功率因数被称为超前功率因数或滞后功率因数。超前功率因数表明了电流会先于电压，能够用来表示电容负载，而滞后功率因数则表明了电流会跟随电压，能够用来表示电感负载。功率因数对消费者向公用事业单位所支付的电费具有有重大影响。

功率因数是有功功率与视在功率的比值。  
它由电压与电流之间的相位差决定，该相位差……

Education

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JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

AC Steady State Power

交流稳态功率

KEY TERMS AND CONCEPTS

关键术语与概念

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...

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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...

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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...

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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 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

Power Factor and AC Load Behavior

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