INTERRUPTION OF SMALL INDUCTIVE CURRENTS POWER CIRCUIT BREAKER BASIC AND TUTORIALS

This occurs (see Fig. 10-67) when disconnecting unloaded transformers, reactors, or compensating coils. An arc is produced between the contacts when the circuit breaker is opened.

  FIGURE 10-67 Principleof small inductive- current interruption; equivalent circuit; typical shape of current and voltage.

The arc voltage is approximately constant at higher currents, since the arc energy is removed only be convection. With small currents, the arc voltage increases as a result of arc looping and a change in the cooling mechanism.

When approaching current zero, the arc current begins to oscillate as a result of interaction with the system; that is it becomes unstable.

As a result of the high oscillation frequency, the current interruption may occur prior to the natural zero passage, can be regarded as instantaneous, and is called current chopping. The chopping current is affected not only by the properties of the circuit breaker but also to a great extent by the system parameters.

Energy at the disconnected load side (L) oscillates with the natural frequency of the capacitances local to the circuit breaker. The maximum voltage is attained at the moment when all the energy is converted into capacitive energy.

As a result of the resistive losses, the voltage on the disconnected load side decays to zero. During current chopping, the breaker is stressed by the supply-side voltage on one side and by the load voltage on the other side.

The supply side voltage is at a maximum, since the load is highly inductive. The load side voltage is the oscillating voltage as the energy exchanges from inductive energy to capacitive energy.

This load side voltage will have a high frequency of up to several thousand cycles per second. During this increasing stress, reignition across the breaker may occur. However, the arc is immediately extinguished again because of the low current and the process begins anew.

Hence, the reignition also helps reduce the energy stored in the disconnected circuit.

CAGE INDUCTION MOTOR BASIC INFORMATION AND TUTORIALS

This simplest form of ac induction motor or asynchronous motor is the basic, universal workhorse of industry. Its general construction is shown in Fig. 10.7. It is usually designed for fixed-speed operation, larger ratings having such features as deep rotor bars to limit

Direct on Line (DOL) starting currents. Electronic variable speed drive technology is able to provide the necessary variable voltage, current and frequency that the induction motor requires for efficient, dynamic and stable variable speed control.

Modern electronic control technology is able not only to render the ac induction motor satisfactory for many modern drive applications but also to extend greatly its application and enable users to take advantage of its low capital and maintenance costs. More striking still, microelectronic developments have made possible the highly dynamic operation of induction motors by the application of flux vector control.

The practical effect is that it is now possible to drive an ac induction motor in such a way as to obtain a dynamic performance in all respects better than could be obtained with a phase-controlled dc drive combination.

The stator winding of the standard industrial induction motor in the integral kilowatt range is three phase and is sinusoidally distributed. With a symmetrical three-phase supply connected to these windings, the resulting currents set up, in the air-gap between the stator and the rotor, a travelling wave magnetic field of constant magnitude and moving at synchronous speed.

The rotational speed of this field is f/p revolutions per second, where f is the supply frequency (hertz) and p is the number of pole pairs (a four-pole motor, for instance, having two pole pairs). It is more usual to express speed in revolutions per minute, as 60 f/p (rpm).

The emf generated in a rotor conductor is at a maximum in the region of maximum flux density and the emf generated in each single rotor conductor produces a current, the consequence being a force exerted on the rotor which tends to turn it in the direction of the flux rotation.

The higher the speed of the rotor, the lower the speed of the rotating stator flux field relative to the rotor winding, and therefore the smaller is the emf and the current generated in the rotor cage or winding.

The speed when the rotor turns at the same rate as that of the rotating field is known as synchronous speed and the rotor conductors are then stationary in relation to the rotating flux. This produces no emf and no rotor current and therefore no torque on the rotor.

Because of friction and windage the rotor cannot continue to rotate at synchronous speed; the speed must therefore fall and as it does so, rotor emf and current, and therefore torque, will increase until it matches that required by the losses and by any load on the motor shaft.

The difference in rotor speed relative to that of the rotating stator flux is known as the slip. It is usual to express slip as a percentage of the synchronous speed. Slip is closely proportional to torque from zero to full load.

The most popular squirrel cage induction motor is of a 4-pole design. Its synchronous speed with a 50 Hz supply is therefore 60 f/p, or 1500 rpm. For a full-load operating slip of 3 per cent, the speed will then be (1 – s)60 f/p, or 1455 rpm.

SINGLE PHASE INDUCTION MOTOR TRANSIENTS BASIC INFORMATION

Single-phase induction motors undergo transients during starting, load perturbation or voltage sags etc. When inverter fed, in variable speed drives, transients occur even for mechanical steady state during commutation mode.

To investigate the transients, for orthogonal stator windings, the cross field (or d-q) model in stator coordinates is traditionally used. [1] In the absence of magnetic saturation, the motor parameters are constant.

Skin effect may be considered through a fictitious double cage on the rotor. The presence of magnetic saturation may be included in the d-q model through saturation curves and flux linkages as variables.

Even for sinusoidal input voltage, the currents may not be sinusoidal. The d-q model is capable of handling it. The magnetisation curves may be obtained either through special flux decay standstill tests in the d-q (m.a) axes (one at a time) or from FEM-in d.c. with zero rotor currents.

The same d-q model can handle nonsinusoidal input voltages such as those produced by a static power converter or by power grid polluted with harmonics by other loads nearby.

To deal with nonorthogonal windings on stator, a simplified equivalence with a d-q (orthogonal) winding system is worked out. Alternatively a multiple reference system + - model is used [3]

While the d - q model uses stator coordinates, which means a.c. During steady state, the multiple reference model uses + - synchronous reference systems which imply d.c. steady state quantities.

Consequently, for the investigation of stability, the frequency approach is typical to the d-q model while small deviation linearization approach may be applied with the multiple reference + - model.

Finally, to consider the number of stator and rotor slots-that is space flux harmonics-the winding function approach is preferred. [4] This way the torque/speed deep around 33% of no load ideal speed, the effect of the relative numbers of stator and rotor slots, broken bars, rotor skewing may be considered.

Still saturation remains a problem as superposition is used. A complete theory of single phase IM, valid both for steady-state and transients, may be approached only by a coupled FEM-circuit model, yet to be developed in an elegant computation time competitive software.  

SYNCHRONOUS INDUCTION MOTORS BASIC INFORMATION AND TUTORIALS

There are three types of motors that can start and run as induction motors yet can lock into the supply frequency and run as synchronous motors as well. They are (1) the wound-rotor motor with dc exciter (2) the permanent-magnet (PM) synchronous motor, and (3) the reluctance-synchronous motor.

The latter two types have been used primarily with adjustable frequency inverter power supplies. In Europe, wound-rotor induction motors have often been provided with low-voltage dc exciters that supply direct current to the rotor, making them operate as synchronous machines.

With secondary rheostats for starting, such a motor gives the low starting current and high torque of the wound-rotor induction motor and an improved power factor under load.

Several different forms of these synchronous induction motors have been proposed, but they have not shown any net advantage over usual salient-pole synchronous or induction machines and are very seldom used in the United States.

  

FIGURE 20-44 Cross section of (a) a conventional PM synchronous motor and (b) a reluctance synchronous motor.

The PM synchronous motor is shown in Fig. 20-44a. The construction is the same as that of an ordinary squirrel-cage motor (either single or polyphase), except that the depth of rotor core below the squirrel cage bars is very shallow, just enough to carry the rotor flux under locked-rotor conditions.

Inside this shallow rotor core is placed a permanent magnet, fully magnetized. The rotor core serves as a keeper, so that the rotor is not demagnetized by removing it from the stator. In starting, the rotor flux is confined to the laminated core.

As the speed rises, the rotor frequency decreases and the rotor flux builds up, creating a pulsating torque with the field of the magnet, as when a synchronous motor is being synchronized after the dc field has been applied. As the motor approaches full speed, therefore, the ac impressed field locks into step with the field of the magnet and the machine runs as a synchronous motor. The absence of rotor I2R loss, the synchronous speed operation, and the high efficiency and power factor make the motor very attractive for special applications, such as high-frequency spinning motors.

When many such motors are supplied from a high-frequency source, the kVA requirements are reduced to perhaps 50% of those needed for usual induction motor types, with consequent large savings.

If the rotor surface of a P-pole squirrel-cage motor is cut away at symmetrically spaced points, forming P salient poles, the motor will accelerate to full speed as an induction motor and then lock into step and operate as a synchronous motor.

The synchronizing torque is due to the change in reluctance and, therefore, in stored magnetic energy, when the air-gap flux moves from the low- into the high-reluctance region. Such motors are often used in small-horsepower sizes, when synchronous operation is required, but they have inherently low pull out torque and low power factor, and also poor efficiency, and therefore require larger frames than the same horsepower induction motor.

The PM synchronous motor has superior performance in every way, except possibly cost. A cross section of the reluctance-synchronous motor is shown in Fig. 20-44b. These motors are available up to about 5 hp.

If the number of rotor salients is nP, instead of P, and if the P-pole motor winding is arranged to also produce a field of (n - 1)P or (n - 1)P poles, the motor may lock into step at a subsynchronous speed and run as a subsynchronous motor. For the P-pole fundamental mmf, acting on the varying rotor permeance will create (n + 1)P and (n - 1) P-pole fields from this case, and these will lock into step with the independently produced (n - 1)P- or (n + 1)P-pole field, when the rotor speed is such as to make the two harmonic fields turn at the same speed in the same direction.

It is difficult to provide much torque in such subsynchronous motors, and their use is therefore limited to very small sizes, such as may be used in small timer or instrument motors.

LENZ'S LAW BASIC DEFINITION AND TUTORIALS

What is Lenz's Law?

Faraday’s law says that the induced emf is given by

V = - dψ/dt

The direction of the induced emf is given by Lenz’s law, which says that the induced voltage is in the direction such that, if the voltage caused a current to flow in the wire, the magnetic field produced by this current would oppose the change in ψ. The negative sign indicates the opposing nature of the emf.

A current flowing in a simple coil produces a magnetic field. Any change in the current will change the magnetic field, which will in turn induce a back-emf in the coil. The self-inductance or just inductance L (H) of the coil relates the induced voltage to the rate of change of current

V = L dI/dT

Two coils placed close together will interact. The magnetic field of one coil will link with the wire of the second. Changing the current in the primary coil will induce a voltage in the secondary coil, given by the mutual inductance M (H)

V2 = M dI1/dT

Placing the coils very close together, on the same former, gives close coupling of the coils. The magnetic flux linking the primary coil nearly all links the secondary coil. The voltages induced in the primary and secondary coils are each proportional to their number of turns, so that

V1/V2 = N1/N2

and by conservation of energy, approximately

I1/I2 = N2/N1

A two-winding transformer consists of two coils wound on the same ferromagnetic core. An autotransformer has only one coil with tapping points. The voltage across each section is proportional to the number of turns in the section.

INDUCTION GENERATOR BASIC INFORMATION AND TUTORIALS

If a machine of this type is connected to a supply, it accelerates as a motor up to a speed near its synchronous speed. If the machine is driven faster than the synchronous speed by an engine or other prime mover, the machine torque reverses and electrical power is delivered by the machine (now acting as a generator) into the connected circuit.

A simple form of wind turbine generator uses an induction machine driven by the wind turbine. The induction machine is first connected to the three-phase supply, and acting as a motor it accelerates the turbine up to near the synchronous speed. At this point, the torque delivered by the wind turbine is sufficient to accelerate the unit further, the speed exceeds the synchronous speed and the induction machine becomes a generator.

It is also possible to operate an induction machine as a generator where there is no separate mains supply available. It is necessary in this case to self-excite the machine, and this is done by connecting capacitors across the stator winding as shown in Fig. 5.20(a).

The leading current circulating through the capacitor and the winding produces a travelling wave of mmf acting on the magnetic circuit of the machine. This travelling wave induces currents in the rotor cage which in turn produces the travelling flux wave necessary to induce the stator voltage.

For this purpose, some machines have an excitation winding in the stator which is separate from the main stator output winding. Figure 5.20(b) shows a single-phase version of the capacitor excitation circuit.

In small sizes, the induction generator can provide a low-cost alternative to the synchronous generator, but it has a relatively poor performance when supplying a low power factor load.

Although induction generators have useful characteristics for use in combination with wind turbines, the magnetizing current must be supplied by other generators running in parallel, or capacitors connected across the stator windings.

Another problem is that the efficiency of an induction generator drops if its speed differs significantly from the synchronous speed, due to high rotor copper loss in the rotor cage.

This can be overcome by using a slipring-fed wound rotor combined with a power electronic converter connected between the stator and rotor windings. Such schemes are often referred to as slip energy recovery using a doubly fed induction generator.

The slip s, of an induction machine is the per unit difference between the rotor speed and the synchronous speed given by:

s = (Ns − Nr)/Ns (5.8)

where Ns is the synchronous speed and Nr is the rotor speed. It can be shown that if Tr is the mechanical torque supplied by a turbine to the rotor of the induction generator, the generated electrical stator power transferred across the air gap is given by TrNs.

Since the input mechanical power to the generator is TrNr, the difference TrNr − TrNs must be the power lost in the rotor, produced mainly by copper loss in the cage. By substitution from eqn 5.8: power transfer to stator = TrNs = rotor loss/s.

With a simple squirrel cage rotor therefore the slip must be low to avoid high rotor loss with a resultant low efficiency.

If the cage is replaced by a three-phase winding, and sliprings are fitted, the same power balance can be achieved by removing the generated rotor power via the sliprings. This power can then be returned to the stator of the generator via a frequency converter. The rotor generated frequency is given by the stator frequency times slip ( f × s).

Fig. 5.20 Self-excitation of an induction generator (a) three phase (b) single phase

INDUCTION GENERATORS - GENERAL CHARACTERISTICS BASIC AND TUTORIALS

An induction or asynchronous generator is one that operates without an independent source for its rotor field current, but in which the rotor field current appears by electromagnetic induction from the field of the armature current.

 The rotor field then interacts with the stator field to transmit mechanical torque just as it does in a synchronous generator, regardless of the fact that it was the stator field that created it (the rotor field) in the first place.

This may seem reminiscent of pulling yourself up by your own bootstraps, but it does actually work. The catch is that some armature current must be provided externally; thus, an induction generator cannot be started up without being connected to a live a.c. system. Another practical concern is that, as we show later in this chapter, induction generators can only operate at leading power factors. For both reasons, their use is quite limited.

Their one important application in power systems is in association with wind turbines. In this case, induction generators offer an advantage because they can readily absorb the erratic fluctuations of mechanical power delivered by the wind resource.

They also cost less than synchronous machines, especially in the size range up to one megawatt. In terms of mechanical operation, the most important characteristic of the induction generator is that the rate of rotation is not fixed, as in the case of the synchronous generator, but varies depending on the torque or power delivered.

The reference point is called the synchronous speed, which is the speed of rotation of the armature magnetic field (corresponding to the a.c. frequency) and also the speed at which a synchronous rotor would spin. The more power is being generated, the faster the induction rotor spins in relation to the synchronous speed; the difference is called the slip speed and typically amounts to several percent.

The rotor may also spin more slowly than the armature speed, but in this case, the machine is generating negative power: it is operating as a motor! While induction machines are usually optimized and marketed for only one purpose, either generating or motoring, they are all in principle reversible. (The same is true for synchronous machines, though their design tends to be even more specialized.)

Figure below shows a curve of torque versus slip speed for a generic induction machine. Zero slip corresponds to synchronous speed, and at this point, the machine delivers no power at all: neglecting friction, it spins freely in equilibrium.

This is called a no-load condition. If a forward torque is exerted on the rotor in this equilibrium state (say, by a connected turbine), it accelerates beyond synchronous speed and generates electric power by boosting the terminal voltage. If the rotor is instead restrained (by a mechanical load), it slows down below synchronous speed and the machine is operating as a motor.

Now we call the torque on the rotor negative, and it acts to push whatever is restraining it with power derived from the armature current and voltage.

The synchronous speed of a given induction machine may be equal to the a.c. frequency (3600 rpm for 60 Hz; 3000 rpm for 50 Hz) or some even fraction thereof (such as 900 or 1800 rpm), depending on the number of magnetic poles, which in this case are created by the armature conductor windings instead of the rotor.

Note that unlike the synchronous generator, where the stator magnetic field has two poles but the rotor field may have any even number of poles, an induction generator must have the same number of poles in the rotor and stator field (because there is no independent excitation).

WHAT ARE INDUCTORS? BASIC DEFINITION AND TUTORIALS

To build an inductor, we would take a length of wire and wrap it around a cylinder, like a coil. If we connect this inductor to a DC power supply, then the flow of current through the wire will set up a strong magnetic field through the center of the coil. (Remember the right-hand rule?)

Each turn in the coil reinforces and strengthens the magnetic field. To DC, an inductor — remember, it’s simply a coil of wire — is a direct short. It has no impedance other than the characteristic resistance of the wire.

But if we connect the inductor to an AC source, something very interesting happens. During the positive half cycle, the current sets up a strong magnetic field in one direction. When the current reverses direction during the negative half cycle, the magnetic field that was set up by the positive half cycle does not collapse right away; it takes time.

During the time that the magnetic field is collapsing, it is in direct opposition to the magnetic field that is trying to set up due to the negative half cycle of current. Therefore, the inductor opposes the change of current, providing an impediment to the free flow of current. It acts as a “choke.”

After a short while, the magnetic field collapses completely and the current flowing in the opposite direction sets up the magnetic field again, but in the opposite orientation. Both the current and the magnetic field are constantly changing directions, and the current is constantly impeded.

In our water–electricity analogy, an inductor may be thought of as a large paddle wheel or a turbine blade in a channel of water. When the water flows, it starts the paddle wheel turning, giving it momentum. If the water current suddenly changes direction, the paddle wheel will resist it because it’s turning the other way.

Once the reverse current overcomes the momentum of the wheel it will begin to turn the other way. But it initially resists the change in direction until the momentum is overcome. The same is true of an electrical current. The magnetic field of the inductor is like the momentum in the paddle wheel.

Inductance is measured in henrys, after the American scientist Joseph Henry. But it is often represented in mathematic equations by the letter “L,” after Heinrich Lenz, a Baltic German physicist who advanced the study of inductance. The henry is a very large value; therefore, it is more common for inductors to be measured in millihenries (10-3 henrys or 0.001 henrys).

In a vacuum, the value of an inductor depends on the diameter of the wire or the wire gauge, the diameter of the coil, and the number of turns in the coil. By inserting an iron core in the center of an inductor, the inductance increases in direct proportion to the permeability of the iron core, i.e., the more the magnetic field influences the core material, the higher the inductance.

An inductor offers no impedance to the flow of DC (other than the small resistance of the wire), but it does impede the flow of AC. As the frequency of the alternating current in an inductor increases, so does the impedance. The amount of impedance in an inductor is called inductive reactance, XL, and it is measured in ohms. XL (ohms) = 2πfL, where XL is the inductive reactance, π is pi (3.14), f is the frequency in hertz, and L is the inductance in henrys.

WHAT IS FARADAY'S LAW OF ELECTROMAGNETIC INDUCTION – DEFINITION AND BASIC TUTORIALS

The famous author Isaac Asimov once said, “The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ (I found it!) but, ‘That’s funny. …’ ” That might have been what Faraday thought when he noticed the meter deflection upon connecting and disconnecting the battery.

According to Faraday’s law, in any closed linear path in space, when the magnetic flux #  surrounded by the path varies with time, a voltage is induced around the path equal to the negative rate of change of the flux in webers per second.

V = dp/dt

The minus sign denotes that the direction of the induced voltage is such as to produce a current opposing the flux. If the flux is changing at a constant rate, the voltage is numerically equal to the increase or decrease in webers in 1 s.

The closed linear path (or circuit) is the boundary of a surface and is a geometric line having length but infinitesimal thickness and not having branches in parallel.

It can vary in shape or position. If a loop of wire of negligible cross section occupies the same place and has the same motion as the path just considered, the voltage will tend to drive a current of electricity around the wire, and this voltage can be measured by a galvanometer or voltmeter connected in the loop of wire.

As with the path, the loop of wire is not to have branches in parallel; if it has, the problem of calculating the voltage shown by an instrument is more complicated and involves the resistances of the branches.

Even though he didn’t get the result he was looking for in his earlier experiment— current flowing steadily through the secondary coil — he did see a hint of current flow in the form of a slight needle deflection in the galvanometer.

But it was enough to lead him down the right path to the answer. Eventually, he found that a stationary magnetic field does not induce current in the secondary coil, but that a changing magnetic field does.

When a battery is first connected to a circuit, the magnetic field has to build from zero to its maximum. As the field grows, the lines of flux of the magnetic field cut the turns of wire in the secondary coil, thereby inducing a current.

Faraday deduced that a changing magnetic field whose lines of flux cut through a wire will generate a voltage. The value of the voltage is proportional to the rate of change and the intensity of the magnetic flux. This is known as Faraday’s law of induction.

According to Faraday’s law of induction, it doesn’t matter whether the lines of flux are cutting through the wire or the wire is moving through the lines of flux, as long as they are moving relative to each other. Therefore, a wire can move through a stationary magnetic field or a magnetic field can move through a stationary wire and it will still generate voltage.

What is important is that the wire is not moving parallel relative to the lines of flux (0°), otherwise no lines of flux will be cut and no voltage will be generated. The movement can, however, be somewhere in between parallel and perpendicular (90°) relative to each other; then some lines of flux will be cut and a proportional amount of voltage will be generated.

For example, if a wire is moving at a 60° angle through a magnetic field, then it is cutting half as many lines of flux as another wire traveling at a 90° angle to the magnetic field at the same rate of speed. Therefore, it would generate half the voltage.

WHAT IS ELECTROMAGNETIC INDUCTION – DEFINITION BASICS AND TUTORIALS

Electric current creates a magnetic field, the reverse effect also exists: magnetic fields, in turn, can influence electric charges and cause electric currents to flow. However, there is an important twist: the magnetic field must be changing in order to have any effect.

A static magnetic field, such as a bar magnet, will not cause any motion of nearby charge. Yet if there is any relative motion between the charge and the magnetic field—for example, because either the magnet or the wire is being moved, or because the strength of the magnet itself is changing— then a force will be exerted on the charge, causing it to move.

This force is called an electromotive force (emf) which, just like an ordinary electric field, is distinguished by its property of accelerating electric charges. The most elementary case of the electromotive force involves a single charged particle traveling through a magnetic field, at a right angle to the field lines (the direction along which iron filings would line up).

This charge experiences a force again at right angles to both the field and its velocity, the direction of which (up or down) depends on the sign of the charge (positive or negative) and can be specified in terms of another right-hand rule, as illustrated in Figure 1.3.

This effect can be expressed concisely in mathematical terms of a cross product of vector quantities (i.e., quantities with a directionality in space, represented in boldface), in what is known as the Lorentz equation, F = ¼ qv X B where F denotes the force, q the particle’s charge, v its velocity, and B the magnetic field.

In the case where the angle between v and B is 908 (i.e., the charge travels at right angles to the direction of the field) the magnitude or numerical result for F is simply the arithmetic product of the three quantities. This is the maximum force possible: as the term cross product suggests, the charge has to move across the field in order to experience the effect.

The more v and B are at right angles to each other, the greater the force; the more closely aligned v and B are, the smaller the force. If v and B are parallel—that is, the charge is traveling along the magnetic field lines rather than across them—the force on the charge is zero. Figure 1.3 illustrates a typical application of this relationship.

The charges q reside inside a wire, being moved as a whole so that each of the microscopic charges inside has a velocity v in the direction of the wire’s motion. If we align our right hand with that direction v and then curl our fingers in the direction of the magnetic field B (shown in the illustration as pointing straight back into the page), our thumb will point in the direction of the force F on a positive test charge.

Because in practice the positive charges in a metal cannot move but the negatively charged electrons can, we observe a flow of electrons in the negative or opposite direction of F. 

Because only the relative motion between the charge and the magnetic field matters, the same effect results if the charge is stationary in space and the magnetic field is moved (e.g., by physically moving a bar magnet), or even if both the magnet and the wire are stationary but the magnetic field is somehow made to become stronger or weaker over time.

The phenomenon of electromagnetic induction occurs when this electromagnetic force acts on the electrons inside a wire, accelerating them in one direction along the wire and thus causing a current to flow. The current resulting from such a changing magnetic field is referred to as an induced current.

This is the fundamental process by which electricity is generated, which will be applied over and over within the many elaborate geometric arrangements of wires and magnetic fields inside actual generators.

INDUCTANCE - BASIC ELECTRICAL PARAMETERS INFORMATION AND TUTORIALS

What Is Inductance?


The basic inductive device is a coil of wire, called an inductor or a solenoid. Its functioning is based on the physical fact that an electric current produces a magnetic field around it.

This magnetic field describes a circular pattern around a current-carrying wire; the direction of the field can be specified with a “right-hand rule.” When a wire is coiled up as shown in figure below, it effectively amplifies this magnetic field, because the contributions from the individual loops add together.

The sum of these contributions is especially great in the center, pointing along the central axis of the coil. The resulting field can be further amplified by inserting a material of high magnetic permeability (such as iron) into the coil; this is how an electromagnet is made.


When such a coil is placed in an a.c. circuit, a second physical fact comes into play, namely, that a changing magnetic field in the vicinity of a conducting wire induces an electric current to flow through this wire. If the current through the coil oscillates back and forth, then so does the magnetic field in its center.

Because this magnetic field is continuously changing, it induces another current in the coil. This induced current is proportional to the rate of change of the magnetic field. The direction of the induced current will be such as to oppose the change in the current responsible for producing the magnetic field.

In other words, the inductor exerts an inhibitive effect on a change in current flow. This inhibitive effect results in a delay or phase shift of the alternating current with respect to the alternating voltage. Specifically, an ideal inductor (with no resistance at all) will cause the current to lag behind the voltage by a quarter cycle, or 90 degrees.

This result is difficult to explain intuitively. We will not attempt to detail the specific changes in the current and magnetic field over the course of a cycle. One thing that can readily be seen from the graph, though, is that the current has its maximum at the instant that the magnetic field changes most rapidly.

As the magnetic field increases and decreases during different parts of the cycle, it stores and releases energy. This energy is not being dissipated, only repeatedly exchanged between the magnetic field and the rest of the circuit. This exchange process becomes very important in the context of power transfer. Because the induced current in an inductor is related to the change in the field per unit time, the frequency of the applied alternating current is important.

The higher the frequency, the more rapidly the magnetic field is changing and reversing, and thus the greater the induced current with its impeding effect is. The lower the frequency, the easier it is for the current to pass through the inductor.

A direct current corresponds to the extreme case of zero frequency. When a steady d.c. voltage is applied to an inductor, it essentially behaves like an ordinary piece of wire. After a brief initial period, during which the field is established, the magnetic field remains constant along with the current.

An unchanging magnetic field exerts no further influence on an electric current, so the flow of a steady direct current through a coil of wire is unaffected by the inductive property. Overall, the effect of an inductor on an a.c. circuit is expressed by its reactance, denoted by X (to specify inductive reactance, the subscript L is sometimes added).

The inductive reactance is the product of the angular a.c. frequency7 and the inductance, denoted by L, which depends on the physical shape of the inductor and is measured in units of henrys (H). In equation form, XL = wL

Thus, unlike resistance, the reactance is not solely determined by the intrinsic characteristics of a device. In the context of power systems, however, because the frequency is always the same, reactance is treated as if it were a constant property.

When describing the behavior of electrical devices in the context of circuit analysis, we are generally interested in writing down a mathematical relationship between the current passing through and the voltage drop across the device. For a resistor, this is simply Ohm’s law, V = IR, where the resistance R is the proportionality constant between voltage and current.

It turns out that the inductance L also works as a proportionality constant between current and voltage across an inductor, but in this case the equation involves the rate of change of current, rather than simply the value of current at any given time. Readers familiar with calculus will recognize the notation dI/dt, which represents the time derivative or rate of change of current with respect to time.

Thus, we write V = L dI/dt meaning that the voltage drop V across an inductor is the product of its inductance L and the rate of change of the current I through it. This equation is used in circuit analysis in a manner analogous to Ohm’s law to establish relationships between current and voltage at different points in the circuit, except that it is more cumbersome to manipulate owing to the time derivative.

ELECTROMAGNETIC FIELD AND HEALTH EFFECTS BASIC INFORMATION AND TUTORIALS

What Are The Health Effects Of Electromagnetic Field?


A current flowing through a wire, alternating at 60 cycles per second (60 Hz), produces around it a magnetic field that changes direction at the same frequency. Thus, whenever in the vicinity of electric equipment carrying any currents, we are exposed to magnetic fields.

Such fields are sometimes referred to as EMF, for electromagnetic fields, or more precisely as ELF, for extremely low-frequency fields, since 60 Hz is extremely low compared to other electromagnetic radiation such as radio waves (which is in the megahertz, or million hertz range).

There is some concern in the scientific community that even fields produced by household appliances or electric transmission and distribution lines may present human health hazards. While such fields may be small in magnitude compared to the Earth’s magnetic field, the fact that they are oscillating at a particular frequency may have important biological implications that are as yet poorly understood.

Research on the health effects of EMFs or ELFs continues. Some results to date seem to indicate a small but statistically significant correlation of exposure to ELFs from electric power with certain forms of cancer, particularly childhood leukemia, while other studies have found no effects.

In any case, the health effects of ELFs on adults appear to be either sufficiently mild or sufficiently rare that no obvious disease clusters have been noted among workers who are routinely exposed—and
have been over decades—to vastly stronger fields than are commonly experienced by the general population.

From a purely physical standpoint, the following observations are relevant: First, the intensity of the magnetic field associated with a current in a wire is directly proportional to the current; second, the intensity of this field decreases at a rate proportional to the inverse square of the distance from the wire, so that doubling the distance reduces the field by a factor of about.

The effect of distance thus tends to outweigh that of current magnitude, especially at close range where a doubling may equate to mere inches. It stands to reason, therefore, that sleeping with an electric blanket or even an electric alarm clock on the bedside table would typically lead to much higher exposure than living near high-voltage transmission lines. Measured ELF data are published by many sources.