The power factor, or cosine phi in electrical engineering, is the ratio of active power P (W) to full S (VA): cos (φ) = P / S. It indicates how efficiently this device uses electrical energy.
Ideal load
To explain the physical value of the power factor, we consider an example of calculating the cosine phi for various consumers. Suppose an ideal capacitor is connected to an AC line. Since the alternating voltage continuously changes its polarity, the capacitor will be charged half the time and half - return the stored energy back to the source. As a result, electrons will constantly circulate in the line, but there will be no pure energy transfer. So, there will be voltage and current in the conductor, but there will be no active power. The product of U by I is called imaginary power, because it is just a mathematical number that does not have real physical meaning. In this example, the power factor is 0.
Similarly, the calculation of the cosine phi for a single ideal inductor will lead to cos (φ) = 0, except that its current will lag behind the voltage.
Now consider the opposite extreme case of resistive load. In this case, all the electric energy entering it is consumed and converted into other forms of energy, such as heat. This is an example where the cosine phi in an electrician is 1. All real circuits work somewhere in the gap between these two extremes.
Vector math
In the analysis of circuits, a sinusoidal signal can be represented by a complex number (called a vector), the module of which is proportional to the value of the signal, and the angle is equal to its phase relative to some reference. In linear schemes, the power factor is equal to the cosine phi. In electrical engineering, this is the angle between the phases of voltage and current. These vectors and their corresponding active and reactive power components can be represented as a right triangle. Of course, voltage is an electric field, and current is a stream of electrons, so the so-called angle between their vectors is nothing more than a mathematical quantity. We agreed that the inductive load creates a positive reactive power Q (measured in volt-ampere-reactive, VAR). This is due to the so-called "delayed" coefficient, since the current lags behind the voltage. Similarly, capacitive loading creates a negative Q and “leading” λ.
Nonlinear distortion
Inductors and capacitors are not the only reasons for the low cosine phi. In electrical engineering, this is a common occurrence when (with the exception of the ideal R, L, and C) the electrical circuits are non-linear, especially due to the presence of active components such as rectifiers. In such circuits, the current I (t) is disproportionate to the voltage V (t), even if the latter is a pure sine wave, since I (t) will be periodic but not sinusoidal. According to the Fourier theorem, any periodic function is the sum of sinusoidal waves with frequencies that are multiples of the original. These waves are called harmonics. It can be shown that they do not promote the transfer of clean energy, but increase the current and decrease the coefficient λ. When the voltage is sinusoidal, only the first harmonic I 1 will provide real power. However, its value depends on the phase shift between current and voltage. These facts are reflected in the general formula for calculating the power factor: λ = (I 1 / I) × cos (φ). The first term in this equation is distortion, and the second is bias.
Active and passive compensation
Correction of cosine phi in electrical engineering is any technique of increasing the power factor to 1. In general, cos (φ) can vary from 0 to 1. The higher the power factor, the more efficiently electricity is used. The causes of imperfection are distortions and phase shift between harmonics of voltage and current of the same frequency. Therefore, there are two main categories of power factor correction methods.
Harmonic distortion is caused by non-linear components, such as a rectifier bridge in DC power supplies that connects directly to a large storage capacitor. They can be adjusted at the design stage of the power source by introducing various passive or active compensation schemes. The main source of phase shift UI are industrial induction motors, which in terms of circuitry have an inductive load. The cosine phi of the engine (which at idle drops to 0.1) can be increased by adding external compensating capacitors. At the same time, they must be installed as close to the load as possible in order to avoid reactive power circulation to the place of their placement.
Active reactive power compensation uses active feedback electronic circuits that smooth out the shape of the rectified current curve.
Nonlinear devices generate harmonic oscillations with a frequency of ƒ = 1 / (2π√LC). If it coincides with one of the harmonics, it will increase, which can lead to various consequences, including catastrophic ones. To avoid this, a small inductor is connected in series with the compensating capacitor, which forms the so-called. harmonic bypass filter.
Why increase the power factor?
There are several reasons for adjusting the cosine phi for various consumers. It is known that when λ <1, alternating currents circulate in the line, which do not transmit active power, but cause heat dissipation in the wiring, create an additional load on the generators and require larger power generating equipment. This is why power companies may charge large customers extra at λ <0.95, bill for full capacity, or fine for excess reactive power. Thus, for an industrial facility, the compensation of the imaginary component can be beneficial.
Correction λ in everyday life
As for electronics, there are rules that limit the harmonics brought by household appliances (PCs, televisions, etc.) to the network. Despite the absence of international standards that directly regulate the power factor, its correction automatically reduces harmonic distortion. Thus, for developers of power supplies, the main reason for increasing the cosine of the phi transformer is the satisfaction of a specific requirement for the harmonic content, even if it can not provide any direct benefits for either the manufacturer or the user.
In everyday life, low λ reduces the throughput of conductors and circuit breakers. In addition to this, contrary to the common misconception of people unfamiliar with the basics of electrical engineering, homeowners and consumers do not benefit from the correction of the power factor.
Imaginary benefit
A number of “appliances” are being produced via the Internet, whose sellers claim that they will cut electricity bills by adjusting the power factor in the home electrical network. They are advertised under different names. In this regard, consumers often ask if reactive power compensation will reduce electricity bills? Indeed, correction λ reduces the total current consumption and, accordingly, reduces Q. However, at present, reactive power is not charged in residential buildings. Knowledge of the basics of electrical engineering avoids the fate of the victims of such deception.
Is it necessary to compensate for Q?
Consumers pay exclusively for active energy, that is, for kilowatt hours, and this is the only thing that old-fashioned rotary meters can measure. Technically, reducing the reactive component will slightly reduce cable losses between the utility meter and the connection point of the imaginary power compensator, but this effect is negligible. By and large, an improvement in the coefficient λ and a decrease in the imaginary current have practically no effect on the meter reading. Theoretically, the situation will change if domestic tariffs include a fee for kilovolt-ampere hours, measured by modern meters, but this is unlikely. Of course, it is profitable for electric companies to lower Q, but first you need to determine the indicators of home workload so as not to do more harm than good.
Do I need built-in expansion joints?
For the same reasons, it makes no sense to buy equipment with built-in power factor correction. In fact, an active compensation system even increases costs due to the addition of a conversion stage. Thus, ceteris paribus, electricity consumption may increase. However, power factor correction in electronics provides certain technical benefits. In particular, this increases the number of watts that can be removed from the outlet. Another advantage is that the devices can operate at any voltage (115 or 230 V). But is it worth the extra cost?