We know that all generators are rotating machines and the resulting voltage is a sine wave. This is what we call AC. One of the advantages of AC power is that it can be changed by a transformer to change its voltage, and it can be raised to hundreds of thousands of volts for long-distance transmission to reduce the loss in transmission. After the destination, it will be reduced to become our common city. Electricity. Our current utility is 220V, 50Hz AC. In electrical engineering, alternating current can be represented by vectors. The vector can represent voltage as well as current. For a purely resistive load, the voltage and current are in phase, while for a pure capacitive load or a purely inductive load, the current and voltage are out of phase, but have a phase angle of 90 degrees, or phase difference. In a purely inductive load, the voltage on it is 90 degrees ahead of the current, while the voltage on the pure capacitive load is 90 degrees behind the current.
If we use a waveform, the voltage is usually expressed as a cosine wave. If the current lags behind the voltage, it is an inductive load. The leading voltage is a capacitive load.
Figure 1. Relationship between AC voltage and AC current for inductive loads
Because virtually no pure and pure capacitors exist, the actual load can only be called an inductive load or a capacitive load. At this time, there is an angle Ï† between the AC voltage and the AC current. For the inductive load, we call this angle Ï† _{L} , and for the capacitive load, the angle is called Ï† _{C} . (See Figure 2)
Figure 2. Vector representation of inductive and capacitive load voltages and currents
The power is equal to the product of voltage and current, but only for purely resistive loads (voltage and current are in phase), and for inductive or capacitive loads, the vector of current is projected onto the voltage vector (horizontal axis). That is, multiply by cosÏ† _{L} or cosÏ† _{C} . We usually refer to this cosÏ† _{L} or cosÏ† _{C} as the power factor.
However, since this angle can be positive or negative, the power factor can also be positive (inductive load) or negative (capacitive load).
But when we use vectors to represent voltage and current, the premise is that their frequencies must be identical. And it is in a linear system.
In linear systems we also express the power factor as the ratio of active power to apparent power. The so-called active power is the product of the voltage and current rms value of the same phase as the current. The apparent power is the "power" obtained by directly multiplying the effective values â€‹â€‹of the voltage and the current without considering the phase difference therebetween. The ratio of the two is obviously the cosine cosÏ† of the phase angle mentioned above.
Some people have tested the power consumption and power factor of various household appliances. The results are as follows:
These data are of course only for reference.
It should be noted:
We know that incandescent lamps are a pure resistor and its power factor is of course equal to one. But this is not the case with the use of more and more fluorescent lamps and energy-saving lamps that have been promoted recently by the state. Fluorescent lamps have long been activated with a large inductor and a starter. After lighting, the large inductor is connected in series in the circuit, so it is basically an inductive load, and its power factor is only 0.51-0.56. After switching to an electronic ballast, the power factor is better, but because the electronic ballast is easy to burn, the most used is the magnetic ballast.
The power factor of the energy-saving lamp is only about 0.54, and it is also an inductive load.
Because the LED is a semiconductor diode, it requires DC power. If it is powered by the mains, there must be a rectifier, usually a diode rectifier bridge. In order to get the smoothest possible DC to avoid ripple flicker, it is usually necessary to add a large electrolytic capacitor. The latter LED can be approximated as a resistor, so the entire circuit is shown in Figure 3.
Figure 3. The equivalent circuit of an LED luminaire
Its various current voltages are shown in Figure 4.
Figure 4. Voltage and current waveforms after bridge rectification and capacitor filtering
The rectified voltage and current waveforms are not sinusoidal, and although the voltage waveform before rectification is a sine wave, the current waveform is not a sine wave. So the whole system is a nonlinear system. The original power factor is defined for the linear system, and the input and output voltage and current are required to be sinusoidal at the same frequency. Otherwise, CosÏ† cannot be used. However, in a non-sinusoidal system, since the voltage and current waveforms are not sinusoidal, there is no phase angle to say. Therefore, the power factor in a nonlinear system must be redefined.
Another definition of power factor as previously described is the ratio of active power to apparent power. Active power refers to the actual output power, while apparent power refers to the product of the input voltage rms value and the input current rms value. This is completely equivalent to CosÏ† in a sine wave system, so there is no problem. But in a nonlinear system, what is active power and what is apparent power is worth exploring.
Because in a nonlinear system, its current waveform has many higher harmonics (see Figure 5).
Figure 5. Current harmonics of a common bridge rectifier
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