Power factor
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The power factor of an AC electric power system is defined as the ratio of the real power to the apparent power.
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[edit] Explanation
In a purely resistive AC circuit, voltage and current waveforms are in step, changing polarity at the same instant in each cycle. Where reactive loads are present, such as with capacitors or inductors, energy storage in the loads result in a time difference between the current and voltage waveforms. Since this stored energy returns to the source and is not available to do work at the load, a circuit with a low power factor will have higher currents to transfer a given quantity of power than a circuit with a high power factor.
In phase - this is analogous to two athletes running around a race track at the same speed and direction, side by side. They pass a point on the track together (simultaneously). Out of phase - this is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time. But the time difference (phase difference) between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds, this would be analogous to two waves of different frequencies. Then, the phase (angle) difference measurement would be meaningless and void.
Real power is the capacity of the circuit for performing work in a particular time. Due to reactive elements of the load, the apparent power, which is the product of the voltage and current in the circuit, will be equal to or greater than the real power. The reactive power is a measure of the stored energy that is reflected to the source during each alternating current cycle.
AC power flow has the three components: real power (P), measured in watts (W); apparent power (S), measured in volt-amperes (VA); and reactive power (Q), measured in reactive volt-amperes (VAr).
The power factor can be expressed as:
- <math>\frac{P}{S}</math>.
In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such that:
- <math>S^2\,\! = {P^2\,\!} + {Q^2\,\!}</math>
If φ is the phase angle between the current and voltage, then the power factor is equal to <math>\left|\cos\phi\right|</math>, and:
- <math> P = S \left|\cos\phi\right| </math>
By definition, the power factor is a dimensionless number between 0 and 1. When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, all the energy supplied by the source is consumed by the load. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle.
The power factor is determined by the type of loads connected to the power system. These can be
- Resistive
- Inductive
- Capacitive
If a purely resistive load is connected to a power supply, current and voltage will change polarity in phase, the power factor will be unity (1), and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as transformers and motors (any type of wound coil) generate reactive power with current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cable generate reactive power with current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, only to send this energy back to the source during the rest of the cycle.
For example, to get 1 kW of real power if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kW ÷ 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor 5 kVA of apparent power needs to be transferred (1 kW ÷ 0.2 = 5 kVA).
It is often possible to adjust the power factor of a system to very near unity. This practice is known as power factor correction and is achieved by switching in or out banks of inductors or capacitors. For example the inductive effect of motor loads may be offset by locally connected capacitors.
Energy losses in transmission lines increase with increasing current. Where a load has a power factor lower than 1, more current is required to deliver the same amount of useful energy. Power companies therefore require that customers, especially those with large loads, maintain the power factors of their respective loads within specified limits or be subject to additional charges. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.
[edit] Non-sinusoidal components
In circuits having only sinusoidal currents and voltages, the power factor effect arises only from the difference in phase between the current and voltage. This is narrowly known as "displacement power factor". The concept can be generalized to a total, distortion, or true power factor where the apparent power includes all harmonic components. This is of importance in practical power systems which contain non-linear loads such as rectifiers, some forms of electric lighting, electric arc furnaces, welding equipment, switched-mode power supplies and other devices.
A particularly important example is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with rated output power ranging from 150W to 500W. Historically, these very low cost power supplies incorporated a simple full wave rectifier that conducted only when the mains instantaneous voltage exceeded the voltage on the input capacitors. This leads to very high ratios of peak to average input current, which also lead to a low distortion power factor and potentially serious phase and neutral loading concerns.
Regulatory agencies such as the EC have set harmonic limits as a method of improving power factor. Declining component cost has hastened acceptance and implementation of two different methods. Normally, this is done by either adding a series inductor (so-called passive PFC) or the addition of a boost converter that forces a sinusoidal input (so-called active PFC). For example, SMPS with passive PFC can achieve power factor of about 0.7...0.75, SMPS with active PFC -- up to 0.99, while SMPS without any power factor correction has power factor of about 0.55...0.65 only.
To comply with current EU standard EN61000-3-2 all switched-mode power supplies with output power more than 75W must include at least passive PFC.
A typical multimeter will give incorrect results when attempting to measure the AC current drawn by a non-sinusoidal load and then calculate the power factor. A true RMS multimeter must be used to measure the actual RMS currents and voltages (and therefore apparent power). To measure the real power or reactive power, a wattmeter designed to properly work with non-sinusoidal currents must be used.
[edit] Mnemonics
English-language power engineering students are advised to remember: "ELI the ICE man" - the voltage E leads the current I in an inductor L, the current leads the voltage in a capacitor C.
Or even shorter: CIVIL - in a Capacitor the I (current) leads V (Voltage), Voltage leads I (current) in an inductor L.
[edit] Power Factor Analogy and FAQ
Power factor is characteristic of alternating current (AC) circuits. Always a value between (0.0) and (1.0), the higher the number the greater/better the power factor.
Circuits containing only heating elements (filament lamps, strip heaters, cooking stoves, etc.) have a power factor of 1.0. Other circuits containing inductive or capacitive elements (ballasts, motors, personal computer, etc.) usually have a power factor below 1.0. Normal power factor ballasts (NPF) typically have a value of (0.4) - (0.6). Ballasts with a power factor greater than (0.9) are considered high power factor ballasts (HPF).
The significance of power factor lies in the fact that utility companies supply customers with volt-amperes, but bill them for watts. The relationship is (watts = volts x amperes x power factor). It is clear that power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the power (watts). This increases generation and transmission costs. Good power factor is considered to be greater than 0.85 or 85%. Utilities may impose penalties on customers who do not have good power factors on their overall buildings. Watts, or real power, is what a customer pays for. VARS is the extra “power” transmitted to compensate for a power factor less than 1.0. The combination of the two is called "apparent" power (VA or volt-amperes).
Consider this popular analogy to clarify the relationship between real and apparent power.
We all know a glass of draft beer generally has a "head" on it. Let's say your favorite pub institutes a new policy - you only pay for the beer, not the foam. While the foam is just aerated beer, it is not really usable in that form. If the glass of beer is half foam, you pay half the price.
This is the same principle as electricity generation - the consumer only pays for the beer (real power), not the foam (the "VARS" mentioned above).
[edit] See also
es:Factor de potencia fr:Facteur de puissance ja:力率 pl:Współczynnik mocy pt:Fator de potência
