Power factor/phase angle

Power factor correction circuits are intended to increase the conduction angle of the rectifiers and to make the ac input current waveform sinusoidal and in phase with the voltage waveform. The input waveforms can be seen in Figure C-2. This means that all the power drawn from the power line is real power and not reactive. The net result is that the peak and RMS current drawn from the line is much lower than that drawn by the capacitive input Alter circuit traditionally used. 

Single-phase active power = El cos 0 Three-phase active power = (3) EI cos 0 where 0 = power factor angle, radians or degrees... 

The power factor of a material may be described loosely as the fraction of the electrical energy stored by the condenser in each cycle which is lost as heat. This arises because the phase difference between voltage and current deviates from 90° (which it would be for a perfect dielectric, e.g. vacuum) by the loss angle, 8. The dissipation factor is the tangent of the loss angle, tan 8. 

The terms displacement and true power factor, are widely mentioned in power factor studies. Displacement power factor is the cosine of the angle between the fundamental voltage and current waveforms. The fundamental waveforms are by definition pure sinusoids. But, if the waveform distortion is due to harmonics (which is very often the case), the power factor angles are different than what would be for the fundamental waves alone. The presence of harmonics introduces additional phase shift between the voltage and the current. True power factor is calculated as the ratio between the total active power used in a circuit (including harmonics) and the total apparent power (including harmonics) supplied from the source ... 

When a heavy atom has been located in the unit cell, its structure factor FH can be used to estimate the relative phase angle FP of the native protein. The value of Ffdepends on the positions and scattering powers of each atom in the unit cell. If anew atom is added, and it does not cause any disruption in the crystal structure, values of the modified structure Fph will be obtained by a vectorial sum as follows ... 

The measurement of power factor and permittivity and the related parameters such as dissipation factor, phase angle, etc., may need to be carried out over a wide range of frequencies from a few Hz to several tens of GHz. However, most measurements are made between 50 Hz and 100 MHz [Brown, 1981]. 

As the three angles u, a and y increase the current waveform moves to the right of the phase voltage waveform. The centre of the current waveform is approximately the position of the peak value of the fundamental current component. Consequently as the current increases the power factor of the fundamental current decreases. Table 15.1 shows values of the harmonic components of current and the power factor as the retardation angle u is increased from zero to 60°. The fundamental component is taken as unity reference at each value of u. 

The sine of the loss angle (sin d) or the cosine of the phase angle (cos 6) is termed the power factor. In electrical applications the power loss (PL) is defined as the rate of energy loss per unit volume and is derived to be... 

ASTM D150 Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation includes the determination of relative permittivity, dissipation factor, loss index, power factor, phase angle, and loss angle through specimens of solid electrical insulating materials when the standards used are lumped impedances. The frequency range that can be covered extends from less than 1 Hz to several hundred megahertz. 

Power factor (p.f.) is defined as the cosine of the phase angle between the... 

Example. We wish to improve a power factor from 85% (lagging) to 90%. We calculate here the rating of a capacitor system per megawatt of delivered power. The phase angle is about 31.8° (cos" 0.85). We must reduce it to cos" 0.90 25.8°. From Eq. (41),... 

Dielectric phase angle n. The angular difference in phase between the alternating voltage (usually sinusoidal) applied to a dielectric and the resulting current. The angle is often symbolized by 9, the cosine of which is the power factor. Ku CC, Liepins R (1987) Electrical properties of polymers. Hanser Publishers, New York. 

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