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# Power factor

Contents
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1 Power factor in linear circuits o 1.1 Definition and calculation o 1.2 Power factor correction of linear loads 2 Non-linear loads o 2.1 Non-sinusoidal components o 2.2 Distortion power factor o 2.3 Switched-mode power supplies o 2.4 Power factor correction in non-linear loads 2.4.1 Passive PFC 2.4.2 Active PFC 3 Importance of power factor in distribution systems 4 Measuring power factor 5 Mnemonics 6 References 7 External links

##  Power factor in linear circuits

Instantaneous and average power calculated from AC voltage and current with a unity power factor ( = 0, cos = 1). Since the blue line is above the axis, all power is real power consumed by the load.

Instantaneous and average power calculated from AC voltage and current with a zero power factor ( = 90, cos = 0). The blue line shows all the power is stored temporarily in the load during the first quarter cycle and returned to the grid during the second quarter cycle, so no real power is consumed.

Instantaneous and average power calculated from AC voltage and current with a lagging power factor ( = 45, cos = 0.71). The blue line shows some of the power is returned to the grid during the part of the cycle labelled In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase), changing polarity at the same instant in each cycle. All the power entering the load is consumed. 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. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in electric or magnetic fields, and then returned to the power grid a fraction of a second later in the cycle. The "ebb and flow" of this nonproductive power increases the current in the line. Thus, a circuit with a low power factor will use higher currents to transfer a given quantity of real power than a circuit with a high power factor. A linear load does not change the shape of the waveform of the current, but may change the relative timing (phase) between voltage and current. Circuits containing purely resistive heating elements (filament lamps, cooking stoves, etc.) have a power factor of 1.0. Circuits containing inductive or capacitive elements (electric motors, solenoid valves, lamp ballasts, and others ) often have a power factor below 1.0.

##  Definition and calculation

AC power flow has the three components: real power (also known as active power) (P), measured in watts (W); apparent power (S), measured in volt-amperes (VA); and reactive power (Q), measured in reactive volt-amperes (var).[3] The power factor is defined as:

. In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such that:

If is the phase angle between the current and voltage, then the power factor is equal to the cosine of the angle, , and:

##  Power factor correction of linear loads

A high power factor is generally desirable in a transmission system to reduce transmission losses and improve voltage regulation at the load. It is often desirable to adjust the power factor of a system to near 1.0. When reactive elements supply or absorb reactive power near the load, the apparent power is reduced. Power factor correction may be applied by an electrical power transmission utility to improve the stability and efficiency of the transmission network. Individual electrical customers who are charged by their utility for low power factor may install correction equipment to reduce those costs. Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying reactive power of opposite sign, adding capacitors or inductors that act to cancel the inductive or capacitive effects of the load, respectively. For example, the inductive effect of motor loads may be offset by locally connected capacitors. If a load had a capacitive value, inductors (also known as reactors in this context) are connected to correct the power factor. In the electricity industry, inductors are said to consume reactive power and capacitors are

said to supply it, even though the reactive power is actually just moving back and forth on each AC cycle. The reactive elements can create voltage fluctuations and harmonic noise when switched on or off. They will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the system's no-load losses. In the worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe overvoltage fluctuations. As such, reactive elements cannot simply be applied without engineering analysis.

1. Reactive Power Control Relay; 2. Network connection points; 3. Slow-blow Fuses; 4. Inrush Limiting Contactors; 5. Capacitors (single-phase or three-phase units, deltaconnection); 6. Transformer Suitable voltage transformation to suit control power (contactors, ventilation,...) An automatic power factor correction unit consists of a number of capacitors that are switched by means of contactors. These contactors are controlled by a regulator that measures power factor in an electrical network. Depending on the load and power factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value. Instead of using a set of switched capacitors, an unloaded synchronous motor can supply reactive power. The reactive power drawn by the synchronous motor is a function of its field excitation. This is referred to as a synchronous condenser. It is started and connected to the electrical network. It operates at a leading power factor and puts vars onto the network as required to support a systems voltage or to maintain the system power factor at a specified level. The condensers installation and operation are identical to large electric motors. Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like an electrically variable capacitor. Unlike capacitors, the amount of reactive power supplied is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensors are often used in connection with high voltage direct current transmission projects or in large industrial plants such as steel mills.

A non-linear load on a power system is typically a rectifier (such as used in a power supply), or some kind of arc discharge device such as a fluorescent lamp, electric welding machine, or

arc furnace. Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. Distortion power factor is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load.

Sinusoidal voltage and non-sinusoidal current give a distortion power factor of 0.75 for this computer power supply load.

##  Non-sinusoidal components

Non-linear loads change the shape of the current waveform from a sine wave to some other form. Non-linear loads create harmonic currents in addition to the original (fundamental frequency) AC current. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system. In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is "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 that 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 typical multimeter will give incorrect results when attempting to measure the AC current drawn by a non-sinusoidal load; the instruments sense the average value of a rectified waveform. The average response is then calibrated to the effective, RMS value. An RMS sensing 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 watt meter designed to work properly with non-sinusoidal currents must be used.

##  Distortion power factor

The distortion power factor describes how the harmonic distortion of a load current decreases the average power transferred to the load.

THDi is the total harmonic distortion of the load current. This definition assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation in practice. I1,rms is the fundamental component of the current and Irms is the total current - both are root mean square-values. The result when multiplied with the displacement power factor (DPF) is the overall, true power factor or just power factor (PF):

##  Switched-mode power supplies

Main article: switched-mode power supply#Power factor A particularly important class of non-linear loads is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with rated output power ranging from a few watts to more than 1 kW. 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 peakto-average input current, which also lead to a low distortion power factor and potentially serious phase and neutral loading concerns. A typical switched-mode power supply first makes a DC bus, using a bridge rectifier or similar circuit. The output voltage is then derived from this DC bus. The problem with this is that the rectifier is a non-linear device, so the input current is highly non-linear. That means that the input current has energy at harmonics of the frequency of the voltage. This presents a particular problem for the power companies, because they cannot compensate for the harmonic current by adding simple capacitors or inductors, as they could for the reactive power drawn by a linear load. Many jurisdictions are beginning to legally require power factor correction for all power supplies above a certain power level. Regulatory agencies such as the EU have set harmonic limits as a method of improving power factor. Declining component cost has hastened implementation of two different methods. To comply with current EU standard EN61000-3-2, all switched-mode power supplies with output power more than 75 W must include passive PFC, at least. 80 PLUS power supply certification requires a power factor of 0.9 or more.[4]

##  Power factor correction in non-linear loads

 Passive PFC The simplest way to control the harmonic current is to use a filter: it is possible to design a filter that passes current only at line frequency (e.g. 50 or 60 Hz). This filter reduces the

harmonic current, which means that the non-linear device now looks like a linear load. At this point the power factor can be brought to near unity, using capacitors or inductors as required. This filter requires large-value high-current inductors, however, which are bulky and expensive. A passive PFC requires an inductor larger than the inductor in an active PFC, but costs less.[5][6] This is a simple way of correcting the nonlinearity of a load by using capacitor banks. It is not as effective as active PFC.[7][8][9][10][11] Passive PFCs are typically more power efficient than active PFCs. Efficiency is not to be confused with the PFC, though many computer hardware reviews conflate them.[7] A passive PFC on a switching computer PSU has a typical power efficiency of around 96%, while an active PFC has a typical efficiency of about 94%.[12]  Active PFC An "active power factor corrector" (active PFC) is a power electronic system that controls the amount of power drawn by a load in order to obtain a power factor as close as possible to unity. In most applications, the active PFC controls the input current of the load so that the current waveform is proportional to the mains voltage waveform (a sine wave). The purpose of making the power factor as close to unity (1) as possible is to make the load circuitry that is power factor corrected appear purely resistive (apparent power equal to real power).[13] In this case, the voltage and current are in phase and the reactive power consumption is zero. This enables the most efficient delivery of electrical power from the power company to the consumer.[14]

Specifications taken from the packaging of a 610W PC power supply showing Active PFC rating Some types of active PFC are:

## Boost Buck Buck-boost

Active power factor correctors can be single-stage or multi-stage. In the case of a switched-mode power supply, a boost converter is inserted between the bridge rectifier and the main input capacitors. The boost converter attempts to maintain a constant DC bus voltage on its output while drawing a current that is always in phase with

and at the same frequency as the line voltage. Another switchmode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics, but permits cheaper and smaller passive components. It is frequently used in practice. For example, SMPS with passive PFC can achieve power factor of about 0.70.75, SMPS with active PFC, up to 0.99 power factor, while a SMPS without any power factor correction has a power factor of only about 0.55 0.65.[15] Due to their very wide input voltage range, many power supplies with active PFC can automatically adjust to operate on AC power from about 100 V (Japan) to 230 V (Europe). That feature is particularly welcome in power supplies for laptops.

##  Importance of power factor in distribution systems

The significance of power factor lies in the fact that utility companies supply customers with volt-amperes, but bill them for watts. Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current. Utilities typically charge additional costs to customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission. With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics.[16] Current Energy Star guidelines for computers (ENERGY STAR Program Requirements for Computers Version 5.0) call for a power factor of 0.9 at 100% of rated output in the PC's power supply. According to a white paper authored by Intel and the U.S. nvironmental rotection gency, PCs with internal power supplies will require the use of active power factor correction to meet the ENERGY STAR 5.0 Program Requirements for Computers.[17] In Europe, IEC 555-2 requires power factor correction be incorporated into consumer products.[18]

##  Measuring power factor

Power factor in a single-phase circuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanced polyphase circuit is not uniquely defined. A direct reading power factor meter can be made with a moving coil meter of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument.

The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque, driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions.[19] Another electromechanical instrument is the polarized-vane type.[20] In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes that are magnetized by the current coil. In operation the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a four-quadrant display of power factor or phase angle. Digital instruments can be made that either directly measure the time lag between voltage and current waveforms and so calculate the power factor, or by measuring both true and apparent power in the circuit and calculating the quotient. The first method is only accurate if voltage and current are sinusoidal; loads such as rectifiers distort the waveforms from the sinusoidal shape.

 Mnemonics
English-language power engineering students are advised to remember: "ELI the ICE man" or "ELI on ICE" the voltage E leads the current I in an inductor L, the current leads the voltage in a capacitor C. Another common mnemonic is CIVIL in a capacitor (C) the current (I) leads voltage (V), voltage (V) leads current (I) in an inductor (L).

## QRP-Measuring RF Voltage, RF Current, RF Power, SWR

This tutorial starts with simple detector circuits, then combines them into an SWR meter. At the end, you should be able to understand and homebrew your own calibrated dummy load, measure RF current and build a SWR-Power meter, all tailored for QRP use. Measuring RF Voltage My meter measures AC volts - why can't I simply measure the output voltage of my rig this way? You can, as long as the frequency is low, perhaps below a few hundred kilohertz. Look at the detailed specs on your AC meter. You'll find that as frequency increases, accuracy goes down. Here's the spec for AC scales on a good quality Fluke 85 handheld multimeter: 60Hz - 0.5% 45Hz to 1KHz - 1.0% 1KHz to 5 Khz - 2.0% 5KHz to 20KHz - 4.0% Above 20KHz., accuracy is not specified, but you can bet it gets worse. We're going to make a simple diode detector circuit that accepts a radio frequency sinewave. The detector will convert it to a DC voltage, which our multimeter can read with good accuracy. What RF voltages would you find at a QRP rig output? Let's take the maximum case of a five-watt QRP rig. This rig will deliver five watts of average power to a 50-ohm resistive dummy load. This five watts is root-mean-square (RMS) power, and we can find the equivalent RMS voltage from P = V2/R. Re-arranging, V(rms) = sqrt(P x R). In our case, V(rms) = sqrt( 5 x 50) = 15.8 volts. Let's find the current too, from P = I2 x R I(rms) = sqrt(5/50) = 0.316 amps(rms). As a check, the voltage divided by the current should be equal to the 50 ohm load resistor, i.e.: 15.8/0.316 = 50 The AC waveforms at the dummy load are sinewaves. Since our multimeter can't measure with any accuracy the amplitude of these waveforms, we'll have to use some electronic circuits to transform AC amplitude to a DC amplitude. Once converted to DC, our multimeter can measure amplitude with good accuracy. Now we have a problem, since we usually require power measurements to be RMS measurements. The electronic circuits required to give DC output proportional to true RMS voltages (or currents) are complex. We have one easy way out...since we're always dealing with sinewaves, we can use a simple peak detector circuit, and scale its output (with a resistor divider, or amplifier) to look like RMS. We won't go through the math (integrating sinewaves isn't fun), but the relationship between the RMS amplitude and peak amplitude of a sinewave is simply this: V(rms) = V(peak) / sqrt(2). Here's a table showing the relationship between RF power, voltages, and currents for a 50 ohm resistive load:

Power out

AC Volts rms

AC Amps rms

AC Volts peak

AC Amps peak

## 0.447 0.283 0.200 0.141 0.0894 0.0632

The electronic circuit to detect peak voltage is quite simple - it involves a diode and capacitor. The diode charges the capacitor up to the peak voltage of the waveform at its input. The capacitor remains charged throughout the sinewaves cycle, so that the voltage across the capacitor is almost entirely a DC voltage. Once the capacitor is charged up to the peak voltage, the diode only needs to conduct enough to keep the capacitor charged. Since our DC multimeter loads this capacitor very little, the diode conducts very little as well, and the RF source sees very little loading due to the diode. So our DC meter should read 22.3 volts(DC) across the peak-detector's capacitor when our 5W transmitter puts out 5W. There is one small error that creeps in...the diode "eats up" some voltage, so that it doesn't quite charge the capacitor as high as it should. Some diodes are better than others in this respect. A schottky diode (or barrier diode) is better than a silicon diode, and a germanium diode is better too. Since these diodes drop almost a constant voltage, then error will be worst for smaller RF voltages. For milliwatters, some effort should be made to compensate for the diode drop. The diode we choose must be a fast switcher. If not, it remains conducting for a bit after the peak, and drags down the capacitor voltage. Diodes meant for 60Hz power supply use are not built for speed, and shouldn't be used in an RF peak detector. Small signal diodes are more appropriate, and almost any germanium small signal diode will do. IN4148, 1N914 are two common silicon types that are fast enough up to 30MHz (at least). 1N34A, 1N270, 1N191 are some common germanium diodes. 1N5711 is a common small-signal schottky diode. Measuring RF Current Once again, our multimeter on AC scales fails at measuring radio-frequency sinewaves. Current measurement is a bit more difficult than voltage measurement shown above. We shall use the same peak-detector circuit, measuring the voltage drop across a small sampling resistor. This resistor will drop a small voltage as RF current flows through it. The peak detector will measure this voltage drop. Ideally, a very small sampling resistor is best: it must be much smaller than the 50 ohm load. If not, the combination of 50 ohm load and series sampling resistor will increase the load seen by the transmitter.

If we were to use a one-ohm sampling resistor (1st circuit), the voltage available (for a 5W

Signal conditioning

Contents
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1 Inputs 2 Signal conditioning processes o 2.1 Filtering o 2.2 Amplifying o 2.3 Isolation 3 References

 Inputs
Signal inputs accepted by signal conditioners include DC voltage and current, AC voltage and current, frequency and electric charge. Sensor inputs can be accelerometer, thermocouple, thermistor, resistance thermometer, strain gauge or bridge, and LVDT or RVDT. Specialized inputs include encoder, counter or tachometer, timer or clock, relay or switch, and other specialized inputs. Outputs for signal conditioning equipment can be voltage, current, frequency, timer or counter, relay, resistance or potentiometer, and other specialized outputs.

##  Signal conditioning processes

Signal conditioning can include amplification, filtering, converting, range matching, isolation and any other processes required to make sensor output suitable for processing after conditioning.

 Filtering

Filtering is the most common signal conditioning function, as usually not all the signal frequency spectrum contains valid data. The common example are 60Hz AC power lines, present in most environments, which will produce noise if amplified.

 Amplifying
Signal amplification performs two important functions: increases the resolution of the inputed signal, and increases its signal-to-noise ratio. For example, the output of an electronic temperature sensor, which is probably in the millivolts range is probably too low for an Analog-to-digital converter (ADC) to process directly. In this case it is necessary to bring the voltage level up to that required by the ADC. Commonly used amplifiers on signal conditioning include Sample and hold amplifiers, Peak Detectors, Log amplifiers, Antilog amplifiers, Instrumentation amplifiers or programmable gain amplifiers.[1]

 Isolation
Signal isolation must be used in order to pass the signal from the source to the measurement device without a physical connection: it is often used to isolate possible sources of signal perturbations. Also notable is that's it is important to isolate the potentially expensive equipment used to process the signal after conditioning from the sensor. Magnetic or optic isolation can be used. Magnetic isolation transforms the signal from voltage to a magnetic field, allowing the signal to be transmitted without a physical connection (for example, using a transformer). Optic isolation takes an electronic signal and modulates it to a signal coded by light transmission (optical encoding), which is then used for input for the next stage of processing. ==Alog-to-digital conversion so they can be read by computerized devices. Other uses include preprocessing signals in order to reduce computing time, converting ranged data to boolean values, for example when knowing when a sensor has reached certain value. Types of devices that use signal conditioning include signal filters, instrument amplifiers, sample-and-hold amplifiers, isolation amplifiers, signal isolators, multiplexers, bridge conditioners, analog-to-digital converters, digital-to-analog converters, frequency converters or translators, voltage converters or inverters, [[pplications== It is primarily utilized for data acquisition, in which sensor signals must be normalized and filtered to levels suitable for anafrequency-to-voltage converter]]s, voltage-to-frequency converters, current-to-voltage converters, current loop converters, and charge converters.
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