Calculating Power Factor

As was mentioned before, the angle of this “power triangle” graphically indicates the ratio between the amount of dissipated (or consumed) power and the amount of absorbed/returned power. It also happens to be the same angle as that of the circuit's impedance in polar form. When expressed as a fraction, this ratio between true power and apparent power is called the power factor for this circuit. Because true power and apparent power form the adjacent and hypotenuse sides of a right triangle, respectively, the power factor ratio is also equal to the cosine of that phase angle. Using values from the last example circuit:



It should be noted that power factor, like all ratio measurements, is a unitless quantity.

For the purely resistive circuit, the power factor is 1 (perfect), because the reactive power equals zero. Here, the power triangle would look like a horizontal line, because the opposite (reactive power) side would have zero length.

For the purely inductive circuit, the power factor is zero, because true power equals zero. Here, the power triangle would look like a vertical line, because the adjacent (true power) side would have zero length.

The same could be said for a purely capacitive circuit. If there are no dissipative (resistive) components in the circuit, then the true power must be equal to zero, making any power in the circuit purely reactive. The power triangle for a purely capacitive circuit would again be a vertical line (pointing down instead of up as it was for the purely inductive circuit).

Power factor can be an important aspect to consider in an AC circuit, because any power factor less than 1 means that the circuit's wiring has to carry more current than what would be necessary with zero reactance in the circuit to deliver the same amount of (true) power to the resistive load. If our last example circuit had been purely resistive, we would have been able to deliver a full 169.256 watts to the load with the same 1.410 amps of current, rather than the mere 119.365 watts that it is presently dissipating with that same current quantity. The poor power factor makes for an inefficient power delivery system.

Poor power factor can be corrected, paradoxically, by adding another load to the circuit drawing an equal and opposite amount of reactive power, to cancel out the effects of the load's inductive reactance. Inductive reactance can only be canceled by capacitive reactance, so we have to add a capacitor in parallel to our example circuit as the additional load. The effect of these two opposing reactances in parallel is to bring the circuit's total impedance equal to its total resistance (to make the impedance phase angle equal, or at least closer, to zero).

Since we know that the (uncorrected) reactive power is 119.998 VAR (inductive), we need to calculate the correct capacitor size to produce the same quantity of (capacitive) reactive power. Since this capacitor will be directly in parallel with the source (of known voltage), we'll use the power formula which starts from voltage and reactance:



Let's use a rounded capacitor value of 22 µF and see what happens to our circuit: (Figure below)



Parallel capacitor corrects lagging power factor of inductive load. V2 and node numbers: 0, 1, 2, and 3 are SPICE related, and may be ignored for the moment.



The power factor for the circuit, overall, has been substantially improved. The main current has been decreased from 1.41 amps to 994.7 milliamps, while the power dissipated at the load resistor remains unchanged at 119.365 watts. The power factor is much closer to being 1:



Since the impedance angle is still a positive number, we know that the circuit, overall, is still more inductive than it is capacitive. If our power factor correction efforts had been perfectly on-target, we would have arrived at an impedance angle of exactly zero, or purely resistive. If we had added too large of a capacitor in parallel, we would have ended up with an impedance angle that was negative, indicating that the circuit was more capacitive than inductive.

A SPICE simulation of the circuit of (Figure above) shows total voltage and total current are nearly in phase. The SPICE circuit file has a zero volt voltage-source (V2) in series with the capacitor so that the capacitor current may be measured. The start time of 200 msec ( instead of 0) in the transient analysis statement allows the DC conditions to stabilize before collecting data. See SPICE listing “pf.cir power factor”.

pf.cir power factor
V1 1 0 sin(0 170 60)
C1 1 3 22uF
v2 3 0 0
L1 1 2 160mH
R1 2 0 60
# resolution stop start
.tran 1m 200m 160m
.end

The Nutmeg plot of the various currents with respect to the applied voltage Vtotal is shown in (Figure below). The reference is Vtotal, to which all other measurements are compared. This is because the applied voltage, Vtotal, appears across the parallel branches of the circuit. There is no single current common to all components. We can compare those currents to Vtotal.



Zero phase angle due to in-phase Vtotal and Itotal . The lagging IL with respect to Vtotal is corrected by a leading IC .

Note that the total current (Itotal) is in phase with the applied voltage (Vtotal), indicating a phase angle of near zero. This is no coincidence. Note that the lagging current, IL of the inductor would have caused the total current to have a lagging phase somewhere between (Itotal) and IL. However, the leading capacitor current, IC, compensates for the lagging inductor current. The result is a total current phase-angle somewhere between the inductor and capacitor currents. Moreover, that total current (Itotal) was forced to be in-phase with the total applied voltage (Vtotal), by the calculation of an appropriate capacitor value.

Since the total voltage and current are in phase, the product of these two waveforms, power, will always be positive throughout a 60 Hz cycle, real power as in Figure above. Had the phase-angle not been corrected to zero (PF=1), the product would have been negative where positive portions of one waveform overlapped negative portions of the other as in Figure above. Negative power is fed back to the generator. It cannont be sold; though, it does waste power in the resistance of electric lines between load and generator. The parallel capacitor corrects this problem.

Note that reduction of line losses applies to the lines from the generator to the point where the power factor correction capacitor is applied. In other words, there is still circulating current between the capacitor and the inductive load. This is not normally a problem because the power factor correction is applied close to the offending load, like an induction motor.

It should be noted that too much capacitance in an AC circuit will result in a low power factor just as well as too much inductance. You must be careful not to over-correct when adding capacitance to an AC circuit. You must also be very careful to use the proper capacitors for the job (rated adequately for power system voltages and the occasional voltage spike from lightning strikes, for continuous AC service, and capable of handling the expected levels of current).

If a circuit is predominantly inductive, we say that its power factor is lagging (because the current wave for the circuit lags behind the applied voltage wave). Conversely, if a circuit is predominantly capacitive, we say that its power factor is leading. Thus, our example circuit started out with a power factor of 0.705 lagging, and was corrected to a power factor of 0.999 lagging.

•REVIEW:
•Poor power factor in an AC circuit may be “corrected”, or re-established at a value close to 1, by adding a parallel reactance opposite the effect of the load's reactance. If the load's reactance is inductive in nature (which is almost always will be), parallel capacitance is what is needed to correct poor power factor.

Read More

How Transformers Operates

Voltage Transformers

A Transformer does not generate electrical power, it transfers electrical power. A transformer is a voltage changer. Most transformers are designed to either step voltage up or to step it down, although some are used only to isolate one voltage from another. The transformer works on the principle that energy can be efficiently transferred by magnetic induction from one winding to another winding by a varying magnetic field produced by alternating current . An electrical voltage is induced when there is a relative motion between a wire and a magnetic field. Alternating current (AC) provides the motion required by changing direction which creates a collapsing and expanding magnetic field.

NOTE: Direct current (DC) is not transformed, as DC does not vary its magnetic fields
A transformer usually consists of two insulated windings on a common iron (steel) core.

The two windings are linked together with a magnetic circuit which must be common to both windings. The link connecting the two windings in the magnetic circuit is the iron core on which both windings are wound. Iron is an extremely good conductor for magnetic fields. The core is not a solid bar of steel, but is constructed of many layers of thin steel called laminations. One of the windings is designated as the primary and the other winding as the secondary. Since the primary and secondary are wound the on the same iron core, when the primary winding is energized by an AC source, an alternating magnetic field called flux is established in the transformer core. The flux created by the applied voltage on the primary winding induces a voltage on the secondary winding. The primary winding receives the energy and is called the input. The secondary winding is discharges the energy and is called the output.



The primary and secondary windings consist of aluminum or copper conductors wound in coils around an iron core and the number of turns in each coil will determine the voltage transformation of the transformer. Each turn of wire in the primary winding has an equal share of the primary voltage . The same is induced in each turn of the secondary. Therefore, any difference in the number of turns in the secondary as compared to the primary will produce a voltage change.

Windings

Step Down Transformers
If there are fewer turns in the secondary winding than in
the primary winding, the secondary voltage will be lower than the primary.


Step Up Transformers
If there are fewer turns in the primary winding than in the secondary winding, the secondary voltage will be higher than the secondary circuit.


Note: The primary winding is the winding which receives the energy; it is not always the high-voltage winding. When the primary winding and the secondary winding have
the same amount of turns there is no change voltage, the ratio is 1/1 unity.


Common single-Phase Voltage Combinations:
120 x 240 to 120/240; 480 to 120/240; 4160 to 240/480
208 to 120/240; 480 to 120/240; 4160 to 240/480
277 to 120/240; 2400 to 120/240
240 x 480 to 120/240; 2400 to 240/480
This relationship between the number of turns in the secondary and primary is often called the turns ratio (also referred to as the voltage ratio). It is customary to specify the turns ratio by writing the primary (input) number first.

Example: 30 to 1 is a step-down transformer, whereas a 1 to 30 would be a step-up transformer.




Winding Physical Location: In most transformers the high voltage winding is wound directly over the low voltage winding to create efficient coupling of the two windings.

Note: Other Designs may have the high voltage winding wound inside, side-by-side or sandwiched between layers of the low voltage winding to meet special requirements.

As stated previously, the voltage transformation is a function of the turns ratio. It may be desirable to change the ratio in order to get rated output voltage when the incoming voltage is slightly different than the normal voltage. As an example, suppose we have a transformer with a 4 to 1 turns ratio. With 480 volts input, the output would be 120 volts. Suppose the line voltage is less than the normal or 456 volts. This would produce an output voltage of 114 volts which is not desirable. By placing a tap in the primary winding, we could change the turns ratio so that with 456 volts input we could still get 120 volts output. This is called primary output voltage tap and standard transformers may have from two to six taps for the purpose of the adjusting to actual line voltages.



The above transformer has a tap (2) 2 1/2% below normal and one at 5% below , it is said to have (2) 2 1/2% full capacity below normal taps (FCBN). This would give a 5% voltage range. When the transformer has taps above normal as shown, they would be full capacity above normal (FCAN).

For Standardization purposes, these taps are in 2 1/2% or 5% steps. The taps are so designed that full capacity output can be obtained when the transformer is set on any of these taps. The universal tap arrangement used on many of our transformers ((2) 2 1/2% FCAN and (4) 2 1/2% FCBN) provides a 15% range of tap voltage adjustments.

Note: taps are only to be used for steady state input line variations. They are not designed to provide a constant secondary voltage when the input line is constantly fluctuating.

Series-Multiple Windings (Reconnectable Transformers)

To make the basic single-phase transformer move versatile, both the primary and secondary windings can be made in two equal parts. The two parts can be reconnected either in a series or in parallel . This provides added versatility as the primary winding can be connected for either 480 volts or 240 volts and the secondary winding can likewise be divided into two equal parts providing either 120 or 240 volts. (note: there will be four leads per winding brought out to the terminal compartment rather than two). Either arrangement will not affect the capacity of the transformer. Secondary windings are rated with a slant such as 120/240 and can be connected in a series for 240V or in a parallel for 120V or 240/120V (for 3-wire operation). Primary windings rated with an X such as 240X480 can operate in series or parallel but are not designed for 3-wire operation. A transformer rated 240X480V primary, 120/240V secondary could be operated in 6 different voltage combinations. Transformers are designed and cataloged by KVA ratings. Just as horsepower ratings designate the power capacity of an electric motor, a transformer’s KVA rating indicates its maximum power output capacity. The higher the transformers KVA rating for a specific input and output voltage, the larger transformer.
What does KVA mean? K= Abbreviation of the Greek word kilo, meaning ‘times 1000 V= Volts A= Amperes or Amp

Calculating KVA. There are only two formulas which you will need to know in order to calculate KVA:

Where:
I = Amps
E = Volts
V3 = 1.732

For Example: A Transformer is supplying a three-phase load that draws 100 amps and requires a supply voltage of 208 volts. Therefore:


Thus, you must select a transformer with a capacity greater than 36.026 KVA.
Alternate Choice Use the FPT full load current rating chart and the secondary voltage on page 3 of the FPT catalog to establish the correct KVA.


Connection: Primary in Series, Secondary in series.
Connection: Primary in Series, Secondary in series.


Connection: Primary in series, Secondary in Parallel.
Connection: Primary in Parallel, Secondary in series


Connection: Primary in Parallel, Secondary in series.
Connection: Primary in Parallel, Secondary in Parallel.

Read More

Why We Use Transformers

Due to the high cost of transmitting electricity at low voltage and high current levels, transformers fulfill a most important role in electrical distribution systems. Utilities distribute electricity over large areas using high voltages, commonly called transmission voltages. Transmission voltages are normally in the 35,000 volt to 50,000 volt range. We know that volts times amps equals watts, and that wires are sized based upon their ability to carry amps. High voltage allows the utility to use small sizes of wire to transmit high levels of power, or watts. You can recognize transmission lines because they are supported by very large steel towers that you see around utility power plants and substations. As this electricity gets closer to its point of use it is converted, through the use of transformers, to a lower voltage normally called distribution voltage. Distribution voltages range from 2,400 to 25,000 volts depending upon the utility. Distribution lines are the ones that feed the pole mount and pad mount transformers located closest to your home or place of business. These transformers convert the distribution voltages to what we call utilization voltages. They are normally below 600 volts and are either single-phase or three-phase and are utilized for operating equipment, including light bulbs and vacuum cleaners in our homes, to motors and elevators where we work. This is the point at which the Dry-Type Distribution Transformer comes into play. It is used to convert the voltage provided by the utility to the voltage we need to operate various equipment.

Read More

Wireless Electricity (WiTricity)

Understanding what WiTricity technology is—transferring electric energy or power over distance without wires—is quite simple. Understanding how it works is a bit more involved, but it doesn’t require an engineering degree. We’ll start with the basics of electricity and magnetism, and work our way up to the WiTricity technology.

Electricity: The flow of electrons (current) through a conductor (like a wire), or charges through the atmosphere (like lightning). A convenient way for energy to get from one place to another!
Illustration of earth's magnetic field


An illustration representing the earth's magnetic field

Magnetism: A fundamental force of nature, which causes certain types of materials to attract or repel each other. Permanent magnets, like the ones on your refrigerator and the earth’s magnetic field, are examples of objects having constant magnetic fields.

Oscillating magnetic fields vary with time, and can be generated by alternating current (AC) flowing on a wire. The strength, direction, and extent of magnetic fields are often represented and visualized by drawings of the magnetic field lines.

Electric current flowing in a wire creates a magnetic field


As electric current, I, flows in a wire, it gives rise to a magnetic field, B, which wraps around the wire. When the current reverses direction, the magnetic field also reverses its direction.

Representation of the magnetic field created when current flows through a coil


The blue lines represent the magnetic field that is created when current flows through a coil. When the current reverses direction, the magnetic field also reverses its direction.

Electromagnetism: A term for the interdependence of time-varying electric and magnetic fields. For example, it turns out that an oscillating magnetic field produces an electric field and an oscillating electric field produces a magnetic field.

Magnetic Induction: A loop or coil of conductive material like copper, carrying an alternating current (AC), is a very efficient structure for generating or capturing a magnetic field.

If a conductive loop is connected to an AC power source, it will generate an oscillating magnetic field in the vicinity of the loop. A second conducting loop, brought close enough to the first, may “capture” some portion of that oscillating magnetic field, which in turn, generates or induces an electric current in the second coil. The current generated in the second coil may be used to power devices. This type of electrical power transfer from one loop or coil to another is well known and referred to as magnetic induction. Some common examples of devices based on magnetic induction are electric transformers and electric generators.

Energy/Power Coupling: Energy coupling occurs when an energy source has a means of transferring energy to another object. One simple example is a locomotive pulling a train car—the mechanical coupling between the two enables the locomotive to pull the train, and overcome the forces of friction and inertia that keep the train still—and, the train moves. Magnetic coupling occurs when the magnetic field of one object interacts with a second object and induces an electric current in or on that object. In this way, electric energy can be transferred from a power source to a powered device. In contrast to the example of mechanical coupling given for the train, magnetic coupling does not require any physical contact between the object generating the energy and the object receiving or capturing that energy.

A transformer uses magnetic induction to transfer power between its windings


An electric transformer is a device that uses magnetic induction to transfer energy from its primary winding to its secondary winding, without the windings being connected to each other. It is used to “transform” AC current at one voltage to AC current at a different voltage.

Resonance: Resonance is a property that exists in many different physical systems. It can be thought of as the natural frequency at which energy can most efficiently be added to an oscillating system. A playground swing is an example of an oscillating system involving potential energy and kinetic energy. The child swings back and forth at a rate that is determined by the length of the swing. The child can make the swing go higher if she properly coordinates her arm and leg action with the motion of the swing. The swing is oscillating at its resonant frequency and the simple movements of the child efficiently transfer energy to the system. Another example of resonance is the way in which a singer can shatter a wine glass by singing a single loud, clear note. In this example, the wine glass is the resonant oscillating system. Sound waves traveling through the air are captured by the glass, and the sound energy is converted to mechanical vibrations of the glass itself. When the singer hits the note that matches the resonant frequency of the glass, the glass absorbs energy, begins vibrating, and can eventually even shatter. The resonant frequency of the glass depends on the size, shape, thickness of the glass, and how much wine is in it.

Resonant Magnetic Coupling: Magnetic coupling occurs when two objects exchange energy through their varying or oscillating magnetic fields. Resonant coupling occurs when the natural frequencies of the two objects are approximately the same.

Two idealized resonant magnetic coils


Two idealized resonant magnetic coils, shown in yellow. The blue and red color bands illustrate their magnetic fields. The coupling of their respective magnetic fields is indicated by the connection of the colorbands.

WiTricity Technology: WiTricity power sources and capture devices are specially designed magnetic resonators that efficiently transfer power over large distances via the magnetic near-field. These proprietary source and device designs and the electronic systems that control them support efficient energy transfer over distances that are many times the size of the sources/devices themselves.

This diagram shows how the magnetic field can wrap around a conductive obstacle


The WiTricity power source, left, is connected to AC power. The blue lines represent the magnetic near field induced by the power source. The yellow lines represent the flow of energy from the source to the WiTicity capture coil, which is shown powering a light bulb. Note that this diagram also shows how the magnetic field (blue lines) can wrap around a conductive obstacle between the power source and the capture device.

Source: WiTricity.com

Read More

Effects at High Frequencies

A direct current flows constantly and uniformly throughout the cross-section of a uniform wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because the acceleration of an electric charge in an alternating current produces waves of electromagnetic radiation that cancel the propagation of electricity toward the center of materials with high conductivity. This phenomenon is called skin effect.

At very high frequencies the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths. The skin depth is the thickness at which the current density is reduced by 63%. Even at relatively low frequencies used for high power transmission (50–60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors. For example, the skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost.

Since the current tends to flow in the periphery of conductors, the effective cross-section of the conductor is reduced. This increases the effective AC resistance of the conductor, since resistance is inversely proportional to the cross-sectional area in which the current actually flows. The AC resistance often is many times higher than the DC resistance, causing a much higher energy loss due to ohmic heating (also called I^2R loss).



Techniques for reducing AC resistance

For low to medium frequencies, conductors can be divided into stranded wires, each insulated from one other, and the relative positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique is called Litz wire. This measure helps to partially mitigate skin effect by forcing more equal current flow throughout the total cross section of the stranded conductors. Litz wire is used for making high-Q inductors, reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher radio frequency current (up to hundreds of kilohertz), such as switch-mode power supplies and radio frequency transformers.

Techniques for reducing radiation loss

As written above, an alternating current is made of electric charge under periodic acceleration, which causes radiation of electromagnetic waves. Energy that is radiated represents a loss. Depending on the frequency, different techniques are used to minimize the loss due to radiation.

Twisted pairs

At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a twisted pair. This reduces losses from electromagnetic radiation and inductive coupling. A twisted pair must be used with a balanced signalling system, so that the two wires carry equal but opposite currents. Each wire in a twisted pair radiates a signal, but it is effectively cancelled by radiation from the other wire, resulting in almost no radiation loss.

Coaxial cables

At frequencies above 1 GHz, unshielded wires of practical dimensions lose too much energy to radiation, so coaxial cables are used instead. A coaxial cable has a conductive wire inside a conductive tube, separated by a dielectric layer. The current flowing on the inner conductor is equal and opposite to the current flowing on the inner surface of the tube. The electromagnetic field is thus completely contained within the tube, and (ideally) no energy is radiation or coupling outside the tube. Coaxial cables have acceptably small losses for frequencies up to about 20 GHz. For microwave frequencies greater than 20 GHz, the losses (due mainly to the dissipation factor of the dielectric) become too large, making waveguides a more efficient medium for transmitting energy.

Waveguides

Waveguides are similar to coax cables, as both consist of tubes, with the biggest difference being that the waveguide has no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. Because waveguides do not have an inner conductor to carry a return current, waveguides cannot deliver energy by means of an electric current, but rather by means of a guided electromagnetic field. Although surface currents do flow on the inner walls of the waveguides, those surface currents do not carry power. Power is carried by the guided electromagnetic fields. The surface currents are set up by the guided electromagnetic fields and have the effect of keeping the fields inside the waveguide and preventing leakage of the fields to the space outside the waveguide.

Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so they are only feasible at microwave frequencies. In addition to this mechanical feasibility, electrical resistance of the non-ideal metals forming the walls of the waveguide cause dissipation of power (surface currents flowing on lossy conductors dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.

Fiber optics

At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the ohmic losses in the waveguide walls become large. Instead, fiber optics, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.

Read More