Hazards of electricity

 Hazards of electricity :

The primary hazards associated with electricity and its use are:

1-  SHOCK. Electric shock occurs when the human body becomes part of a path through which electrons can flow. The resulting effect on the body can be either direct or indirect.

-  Direct. Injury or death can occur whenever electric current flows through the human body. Currents of less than 30 mA can result in death. A thorough coverage of the effects of electricity on the human body is contained in the section of this module entitled Effects of Electricity on the Human Body.

-  Indirect. Although the electric current through the human body may be well below the values required to cause noticeable injury, human reaction can result in falls from ladders or scaffolds, or movement into operating machinery

2- BURNS. Burns can result when a person touches electrical wiring or equipment that is improperly used or maintained. Typically, such burn injuries occur on the hands.

3- ARC-BLAST. Arc-blasts occur from high-amperage currents arcing through air. This abnormal current flow (arc-blast) is initiated by contact between two energized points. This contact can be caused by persons who have an accident while working on energized components, or by equipment failure due to fatigue or abuse. Temperatures as high as 35,000oF have been recorded in arc-blast research. The three primary hazards associated with an arc-blast are:

- Thermal Radiation. In most cases, the radiated thermal energy is only part of the total energy available from the arc. Numerous factors, including skin color, area of skin exposed, type of clothing have an effect on the degree of injury. Proper clothing, work distances and overcurrent protection can improve the chances of curable burns.
- Pressure Wave. A high-energy arcing fault can produce a considerable pressure wave. Research has shown that a person 2 feet away from a 25 kA arc would experience a force of approximately 480 pounds on the front of their body. In addition, such a pressure wave can cause serious ear damage and memory loss due to mild concussions. In some instances, the pressure wave may propel the victim away from the arc-blast, reducing the exposure to the thermal energy. However, such rapid movement could also cause serious physical injury.
- Projectiles. The pressure wave can propel relatively large objects over a considerable distance. In some cases, the pressure wave has sufficient force to snap the heads of 3/8 inch steel bolts and knock over ordinary
construction walls. The high-energy arc also causes many of the copper and aluminum components in the electrical equipment to become molten. These "droplets" of molten metal can be propelled great distances by the pressure wave. Although these droplets cool rapidly, they can still be above temperatures capable of causing serious burns or igniting ordinary clothing at distances of 10 feet or more. In many cases, the burning effect is much worse than the injury from shrapnel effects of the droplets.

4- EXPLOSIONS. Explosions occur when electricity provides a source of ignition for an explosive mixture in the atmosphere. Ignition can be due to overheated conductors or equipment, or normal arcing (sparking) at switch contacts. OSHA standards, the National Electrical Code and related safety standards have preciserequirements for electrical systems and equipment when applied in such areas. 

5- FIRES. Electricity is one of the most common causes of fire both in the home and workplace. Defective or misused electrical equipment is a major cause, with high resistance connections being one of the primary sources of ignition. High resistanceconnections occur where wires are improperly spliced or connected to other components such as receptacle outlets and switches. This was the primary cause of fires associated with the use of aluminum wire in buildings during the 1960s and 1970s. Heat is developed in an electrical conductor by the flow of current at the rate I2R. The heat thus released elevates the temperature of the conductor material. A typical use of this formula illustrates a common electrical hazard. If there is a bad connection at a receptacle, resulting in a resistance of 2 ohms, and a current of 10 amperes flows through that resistance, the rate of heat produced (W) would be:

W = I ^2R = 10^2 x 2 = 200 watts

If you have ever touched an energized 200 watt light bulb, you will realize that this is a lot of heat to be concentrated in the confined space of a receptacle. Situations similar to this can contribute to electrical fires.

Power Factor basic

 Power Factor Fundamentals

Most Industrial loads require both Real power and Reactive power to produce useful work

You pay for BOTH types of power

Capacitors can supply the REACTIVE power thus the utility doesn’t need to

Capacitors save you money!

Why Apply PFC’s?

Power Factor Correction Saves Money!

Reduces Power Bills

Reduces I2R losses in conductors

Reduces loading on transformers

Improves voltage drop

What is PF ?

Introduction:

Most plant loads are Inductive and require a magnetic field to operate:

- Motors

- Transformers

- Florescent lighting

The magnetic field is necessary, but produces no useful work

The utility must supply the power to produce the magnetic field and the power to produce the useful work: You pay for all of it!

These two types of current are the ACTIVE and REACTIVE components

The Basics:

The Power Triangle:

You pay for fuel for the VERTICAL portion of flight, as well as the fuel for the HORIZONTAL portion of flight

Similarly, motors require REACTIVE power to set up the magnetic field while the ACTIVE power produces the useful work (shaft horsepower). Total Power is the vector sum of the two & represents what you pay for:

The Power Triangle:

Power Factor is the ratio of Active Power to Total Power:

Power Factor = Active (Real) Power /Total Power

                      = kW / kVA

                      =  cos(φ)

 Power Factor is a measure of efficiency (Output/Input)

Why do we Install Capacitors?

Capacitors supply, for free, the reactive energy required by inductive loads.

You only have to pay for the capacitor !

Since the utility doesn’t supply it (kVAR), you don’t pay for it!

Utility Supplies Reactive Current

Capacitor Supplies Reactive Current

Other Benefits:

1- Released system capacity:

The effect of PF on current drawn is shown below:

Decreasing size of conductors required to carry the same 100kW load at P.F. ranging from 70% to 100%

2- Reduced Power Losses:

- As current flows through conductors, the conductors heat. This heating is power loss.

- Power loss is proportional to current squared (PLoss=I2 R).

- Current is proportional to P.F.

- Conductor loss can account for as much as 2-5% of total load

3- Capacitors can reduce losses by 1-2% of the total load

4- Voltage Improvement:

- When capacitors are added, voltage will increase

- Typically only a few percent

- Not a significant economic or system benefit

Severe over-correction (P.F.>1) will cause a voltage rise that can damage insulation & equipment; or result
in utility surcharges!

- Usually a result of large fixed capacitors at mains

Summary of Benefits:

1- Reduced Power Costs:

- Since Capacitors supply reactive power, you don’t pay the utility for it

- You can calculate the savings

2- Off-load transformers

- Defer buying a larger transformer when adding loads

3- Reduce voltage drop at loads

- Only if capacitors are applied at loads

- (minimal benefit at best)

What we learned : 

1- Most Industrial loads (i.e. motors)are Inductive and draw REACTIVE power

2- The Utility supplies this energy therefore you pay for it

3- Power Factor Capacitors supply REACTIVE energy thus the utility doesn’t need to

4- Power Factor Capacitors save money

5- There are other benefits to correcting power factor,

6- reduced heating in cables

7- reduced heating in transformer(s)

8- frees up system capacity

AC resistor circuits

AC resistor circuits :

Pure resistive AC circuit: resistor voltage and current are in phase.

If we were to plot the current and voltage for a very simple AC circuit consisting of a source
and a resistor it would look something like this.

Voltage and current “in phase” for resistive circuit..

Because the resistor simply and directly resists the flow of electrons at all periods of time, the waveform for the voltage drop across the resistor is exactly in phase with the waveform for the current through it. We can look at any point in time along the horizontal axis of the plot and compare those values of current and voltage with each other (any “snapshot” look at the values of a wave are referred to as instantaneous values, meaning the values at that instant in time). When the instantaneous value for current is zero, the instantaneous voltage across the resistor is also zero. Likewise, at the moment in time where the current through the resistor is at its positive peak, the voltage across the resistor is also at its positive peak, and so on. At any given point in time along the waves, Ohm’s Law holds true for the instantaneous values of voltage and current.

We can also calculate the power dissipated by this resistor, and plot those values on the
same graph

Instantaneous AC power in a pure resistive circuit is always positive.

Note that the power is never a negative value. When the current is positive (above the line), the voltage is also positive, resulting in a power (p=ie) of a positive value. Conversely, when the current is negative (below the line), the voltage is also negative, which results in a positive value for power (a negative number multiplied by a negative number equals a positive number). This consistent “polarity” of power tells us that the resistor is always dissipating power, taking it from the source and releasing it in the form of heat energy. Whether the current is positive or negative, a resistor still dissipates energy.

reference :
Lessons In Electric Circuits, Volume II – AC By Tony R. Kuphaldt

Armstrong oscillator

 Armstrong oscillator :

The Armstrong oscillator (also known as Meissner oscillator ) is named after the electrical engineer Edwin Armstrong, its inventor. It is sometimes called a tickler oscillator because the feedback needed to produce oscillations is provided using a tickler coil (T in the circuit diagram) via magnetic coupling between coil L and coil T. Assuming the coupling is weak, but sufficient to sustain oscillation, the frequency is determined primarily by the tank circuit (L and C in the illustration) and is approximately given by . In a practical circuit, the actual oscillation frequency will be slightly different from the value provided by this formula because of stray capacitance and inductance, internal losses (resistance), and the loading of the tank circuit by the tickler coil.

This circuit is the basis of the regenerative receiver for amplitude modulated radio signals. In that application, an antenna is attached to an additional tickler coil, and the feedback is reduced, for example, by slightly increasing the distance between coils T and L, so the circuit is just short of oscillation. The result is a narrow-band radio-frequency filter and amplifier. The non-linear characteristic of the transistor or tube provides the demodulated audio signal.

The circuit diagram shown is a modern implementation, using a field-effect transistor as the amplifying element. Armstrong's original design used a vacuum tube triode.

Note that in the Meissner variant, the LC resonant (tank) circuit is exchanged with the feedback coil, i.e. in the output path (Anode, Drain, Collector) of the amplifier, e.g. Grebennikov, Fig.  Many publications, however, embrace both variants with either name; apparently the English speakers using Armstrong, and the German speakers Meibner.

reference : 

http://en.wikipedia.org/wiki/Armstrong_oscillator

Electronic oscillator

 Electronic oscillator :

An electronic oscillator is an electronic circuit that produces a repetitive electronic signal, often a sine wave or a square wave. They are widely used in innumerable electronic devices. Common examples of signals generated by oscillators include signals broadcast by radio and television transmitters, clock signals that regulate computers and quartz clocks, and the sounds produced by electronic beepers and video games.

A low-frequency oscillator (LFO) is an electronic oscillator that generates an AC waveform at a frequency below ≈20 Hz. This term is typically used in the field of audio synthesizers, to distinguish it from an audio frequency oscillator.

Oscillators designed to produce a high-power AC output from a DC supply are usually called inverters.

There are two main types of electronic oscillator: the harmonic oscillator and the relaxation oscillator.

Harmonic oscillator :

The harmonic, or linear, oscillator produces a sinusoidal output. There are a few types of harmonic oscillators.

The basic form of a harmonic oscillator is an electronic amplifier with an electronic filter connected in the feedback loop. When the power supply to the amplifier is first switched on, the amplifier's output consists only of noise. The noise travels around the loop, being filtered and re-amplified until it increasingly resembles the desired signal.

Capacitive-inductive oscillators also known as LC oscillators are built by a tank circuit, which oscillates by charging and discharging a capacitor through an inductor and an active negative resistance circuit that compensates the internal LC losses. These oscillators are typically used when a tunable precision frequency source is necessary, such as with radio transmitters and receivers. Most LC oscillators use off-chip inductors. On-chip inductors suffer large resistive losses, so that the Q-factor of the resulting tank circuit is generally less than 10. As processes have made larger numbers of metal layers available (allowing designers to distance the inductor metal layer from the resistive substrate), on-chip inductors have become more useful.

A piezoelectric crystal (commonly quartz) may take the place of the filter to stabilise the frequency of oscillation, this is called a crystal oscillator. These kinds of oscillators contain quartz crystals that mechanically vibrate between two slightly different shapes. Crystals have very high Q-factor, and can only be tuned within a very small range of frequencies. Because the crystal is an off-chip component, it adds some cost and complexity to the system design, but the crystal itself is generally quite inexpensive.

Surface acoustic wave (SAW) devices are a kind of crystal oscillator, but achieve much higher frequencies by establishing standing waves on the surface of the quartz crystal.^{[citation needed]} These are more expensive than crystal oscillators, and are used in specialized applications which require a direct and very accurate high frequency reference, for example, in cellular telephones.

There are many ways to implement harmonic oscillators, because there are different ways to amplify and filter. Some of the different circuits are:

• Armstrong oscillator
• Hartley oscillator
• Colpitts oscillator
• Clapp oscillator
• Delay line oscillator
• Pierce oscillator (crystal)
• Phase-shift oscillator
• RC oscillator (Wien Bridge and "Twin-T")
• Cross-coupled LC oscillator
• Vackar oscillator
• Opto-Electronic Oscillator.

Relaxation oscillator :

Main article: relaxation oscillator

A relaxation oscillator produces a non-sinusoidal output, such as a square, sawtooth or triangle wave. It contains an energy-storing element (a capacitor or, more rarely, an inductor) and a trigger circuit (a latch, Schmitt trigger, negative resistor, etc.) that periodically charges/discharges the energy stored in the storage element thus causing abrupt changes in the output waveform.

Square-wave relaxation oscillators are used to provide the clock signal for sequential logic circuits such as timers and counters, although crystal oscillators are often preferred for their greater stability. Triangle wave or sawtooth oscillators are used in the timebase circuits that generate the horizontal deflection signals for cathode ray tubes in analogue oscilloscopes and television sets. In function generators, this triangle wave may then be further shaped into a close approximation of a sine wave.

Ring oscillators are built of a ring of active delay stages. Generally the ring has an odd number of inverting stages, so that there is no single stable state for the internal ring voltages. Instead, a single transition propagates endlessly around the ring.

Types of relaxation oscillator circuits include:

• multivibrator
• ring oscillator
• delay line oscillator
• rotary traveling wave oscillator.

Ohm's law

Ohm's law :

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them.

The mathematical equation that describes this relationship is:

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above to explain his experimental results. The above equation is the modern form of Ohm's law.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.

see : http://en.wikipedia.org/wiki/Ohm%27s_law

Water Turbines

Water Turbine

Water turbine is a device that convert the energy in a stream of fluid into mechanical energy by passing the stream through a system of fixed and moving fan like blades and causing the latter to rotate. A turbine looks like a large wheel with many small radiating blades around its rim.

Classification of Water turbines
According to the type of flow of water : The water turbines used as prime movers in hydro electric power stations are of four types.They are

• axial flow : having flow along shaft axis
• inward radial flow : having flow along the radius
• tangential or peripheral : having flow along tangential direction
• mixed flow : having radial inlet axial outlet

If the runner blades of axial flow turbines are fixed,those are called propeller turbines.

According to the action of water on moving blades water turbines are of 2 types namely impulse ad reaction type turbines.
Impulse Turbines :These turbines change the direction of flow of a high velocity fluid jet. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. There is no pressure change of the fluid in the turbine rotor blades. Before reaching the turbine the fluid's Pressure head is changed to velocity head by accelerating the fluid with a nozzle. Pelton wheels and de Laval turbines use this process exclusively. Impulse turbines do not require a pressure casement around the runner since the fluid jet is prepared by a nozzle prior to reaching turbine. Newton's second law describes the transfer of energy for impulse turbines.

Reaction Turbines : These turbines develop torque by reacting to the fluid's pressure or weight. The pressure of the fluid changes as it passes through the turbine rotor blades. A pressure casement is needed to contain the working fluid as it acts on the turbine stage(s) or the turbine must be fully immersed in the fluid flow (wind turbines). The casing contains and directs the working fluid and, for water turbines, maintains the suction imparted by the draft tube. Francis turbines and most steam turbines use this concept. For compressible working fluids, multiple turbine stages may be used to harness the expanding gas efficiently. Newton's third law describes the transfer of energy for reaction turbines.

According to the Head and quantity of water available the water turbines are of 2 types.Those are high head - low flow and low to medium head and high to medium discharge turbines.

According to the name of the originator water turbines are of 3 types namely Pelton Wheel,Francis tubine and Kaplan turbine.

Nuclear Power

Nuclear Power

Nuclear power is the controlled use of nuclear reactions to release energy for work including propulsion, heat, and the generation of electricity. Use of nuclear power to do significant useful work is currently limited to nuclear fission and radioactive decay. Nuclear energy is produced when a fissile material, such as uranium-235 (235U), is concentrated such that nuclear fission takes place in a controlled chain reaction and creates heat — which is used to boil water, produce steam, and drive a steam turbine. The turbine can be used for mechanical work and also to generate electricity. Nuclear power provides 7% of the world's energy and 15.7% of the world's electricity and is used to power most military submarines and aircraft carriers.

The United States produces the most nuclear energy, with nuclear power providing 20% of the electricity it consumes, while France produces the highest percentage of its electrical energy from nuclear reactors—80% as of 2006. In the European Union as a whole, nuclear energy provides 30% of the electricity.Nuclear energy policy differs between countries, and some countries such as Austria, Australia and Ireland have no nuclear power stations.

Concerns about nuclear power

The use of nuclear power is controversial because of the problem of storing radioactive waste for indefinite periods, the potential for possibly severe radioactive contamination by accident or sabotage, and the possibility that its use in some countries could lead to the proliferation of nuclear weapons. Proponents believe that these risks are small and can be further reduced by the technology in the new reactors. They further claim that the safety record is already good when compared to other fossil-fuel plants, that it releases much less radioactive waste than coal power, and that nuclear power is a sustainable energy source. Critics, including most major environmental groups, claim nuclear power is an uneconomic and potentially dangerous energy source with a limited fuel supply, especially compared to renewable energy, and dispute whether the costs and risks can be reduced through new technology.

There is concern in some countries over North Korea and Iran operating research reactors and fuel enrichment plants, since those countries refuse adequate IAEA oversight and are believed to be trying to develop nuclear weapons. North Korea admits that it is developing nuclear weapons, while the Iranian government vehemently denies the claims against Iran.

Several concerns about nuclear power have been expressed, and these include:

• Concerns about nuclear reactor accidents, such as the Chernobyl disaster
• Vulnerability of plants to attack or sabotage
• Use of nuclear waste as a weapon
• Health effects of nuclear power plants
• Nuclear proliferation

Nuclear Energy,Nuclear Fuels

Nuclear Energy

Nuclei are made up of protons and neutron, but the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it. The difference is a measure of the nuclear binding energy which holds the nucleus together.

Nuclear energy is energy released from the atomic nucleus. Atoms are tiny particles that make up every object in the universe. There is enormous energy in the bonds that hold atoms together.This binding energy can be calculated from the Einstein relationship: mass-energy equivalence formula E = mc², in which E = energy, m = mass, and c = the speed of light in a vacuum (a physical constant).The alpha particle gives binding energy of 28.3 MeV

Nuclear energy is released by several processes:

• Radioactive decay, where a radioactive nucleus decays spontaneously into a lighter nucleus by emitting a particle;
• Endothermic nuclear reactions where two nuclei merge to produce two different nuclei. The following two processes are particular examples:
• Fusion, two atomic nuclei fuse together to form a heavier nucleus;
• Fission, the breaking of a heavy nucleus into two nearly equal parts.

Nuclear FuelsNuclear fuel is any material that can be consumed to derive nuclear energy, by analogy to chemical fuel that is burned to derive energy. By far the most common type of nuclear fuel is heavy fissile elements that can be made to undergo nuclear fission chain reactions in a nuclear fission reactor; nuclear fuel can refer to the material or to physical objects (for example fuel bundles composed of fuel rods) composed of the fuel material, perhaps mixed with structural, neutron moderating, or neutron reflecting materials.

Not all nuclear fuels are used in fission chain reactions. For example, 238Pu and some other elements are used to produce small amounts of nuclear power by radioactive decay in radiothermal generators, and other atomic batteries. Light isotopes such as 3H (tritium) are used as fuel for nuclear fusion. If one looks at binding energy of specific isotopes, there can be an energy gain from fusing most elements with a lower atomic number than iron, and fissioning isotopes with a higher atomic number than iron.

The most common fissile nuclear fuels are natural urnium,enriched uranium,plutonium and 233U.Natural uranium is the parent material.The materials 235U,233U and 239Pu are called fissionable materials.The only fissionable nuclear fuel occuring in nature is uraium of which 99.3% is 238U and 0.7% is 235U and 234U is only a trace.Out of these isotopes only 235U will fission in a chain reaction.The other two fissionable materials can be produced artificially from 238U and 232Th which occur in nature are called fertile materials.Out of the three fissionable materials 235U has some advantages over the other two due to its higher fission percentage.Fissionable materials 239Pu and 233U are formed in the nuclear reactors during fission process from 238U and 232Th respectively due to absorption of neutrons with out fission.Getting 239Pu process is called conversion and getting 233U is called breeding.

transmission lines

Classification of transmission lines

Transmission lines are classified as short, medium and long. When the length of the line is less than about 80Km the effect of shunt capacitance and conductance is neglected and the line is designated as a short transmission line. For these lines the operating voltage is less than 20KV.

For medium transmission lines the length of the line is in between 80km - 240km and the operating line voltage wil be in between 21KV-100KV.In this case the shunt capacitance can be assumed to be lumped at the middle of the line or half of the shunt capacitance may be considered to be lumped each end of the line.The two representations of medium length lines are termed as nominal-T and nominal- π respectively.

Lines more than 240Km long and line voltage above 100KV require calculations in terms of distributed parameters.Such lines are known as long transmission lines.This classification on the basis of length is more or less arbitrary and the real criterion is the degree of accuracy required.

Open Circuit and Short Circuit

Open Circuit :
An electric circuit that has been broken, so that there is no complete path for current flow. A condition in an electric circuit in which there is no path for current between two points; examples are a broken wire and a switch in the open, or off, position.

Open-circuit voltage is the potential difference between two points in a circuit when a branch (current path) between the points is open-circuited. Open-circuit voltage is measured by a voltmeter which has a very high resistance (theoretically infinite).

Short Circuit :
A low-resistance connection established by accident or intention between two points in an electric circuit. The current tends to flow through the area of low resistance, bypassing the rest of the circuit.

Common usage of the term implies an undesirable condition arising from failure of electrical insulation, from natural causes (lightning, wind, and so forth), or from human causes (accidents, intrusion, and so forth).

In circuit theory the short-circuit condition represents a basic condition that is used analytically to derive important information concerning the network behavior and operating capability. Thus, along with the open-circuit voltage, the short-circuit current provides important basic information about the network at a given point.

The short-circuit condition is also used in network theory to describe a general condition of zero voltage.

AC Voltage

AC Voltage :
A voltage in which the polarity alternates.

Measuremnt of AC magnitde :

AC voltage alternates in polarity and AC current alternates in direction. We know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a "waveform." We can measure the rate of alternation by measuring the time it takes for a wave to evolve before it repeats itself (the "period"), and express this as cycles per unit time, or "frequency." In music, frequency is the same as pitch, which is the essential property distinguishing one note from another.

One way to express the intensity, or magnitude (also called the amplitude), of an AC quantity is to measure its peak height on a waveform graph. This is known as the peak or crest value of an AC waveform:


Another way is to measure the total height between opposite peaks. This is known as the peak-to-peak (P-P) value of an AC waveform:


This is the measurement in case of a sinusoidal wave either it may be voltage or current. The measurement definition is same fo the ramining wave shapes also.

Average Value :

One way of expressing the amplitude of different waveshapes in a more equivalent fashion is to mathematically average the values of all the points on a waveform's graph to a single, aggregate number. This amplitude measure is known simply as the average value of the waveform. If we average all the points on the waveform algebraically (that is, to consider their sign, either positive or negative), the average value for most waveforms is technically zero, because all the positive points cancel out all the negative points over a full cycle:

This, of course, will be true for any waveform having equal-area portions above and below the "zero" line of a plot. However, as a practical measure of a waveform's aggregate value, "average" is usually defined as the mathematical mean of all the points' absolute values over a cycle.

Root Mean Square (RMS) Value :
RMS value means , first square all the values, then find the average (mean) of these square values over a complete cycle, and find the square root of this average. That is the RMS value.

The value of an AC voltage is continually changing from zero up to the positive peak, through zero to the negative peak and back to zero again. Clearly for most of the time it is less than the peak voltage, so this is not a good measure of its real effect.

Instead we use the root mean square voltage (VRMS) which is 0.7 of the peak voltage (Vpeak):
VRMS = 0.7 × Vpeak and Vpeak = 1.4 × VRMS
These equations also apply to current. They are only true for sine waves (the most common type of AC) because the 0.7 and 1.4 are different values for other shapes.

The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. AC voltmeters and ammeters show the RMS value of the voltage or current.

For pure Sinusoidal : RMS = 0.707 (Peak) , AVG = 0.637 (Peak) , P-P = 2 (Peak).
For pure Square : RMS = Peak , AVG = Peak , P-P = 2 (Peak).
For pure Triangular : RMS = 0.577 (Peak) , AVG = 0.5 (Peak) , P-P = 2 (Peak).

The Crest factor of an AC wave form for instance is given by
Crest factor = Peak Value / RMS Value

The form factor of an AC waveform is the ratio of its peak value divided by its average value
Form factor = Peak Value / Average ValueFor more details visit the following sites :
http://www.allaboutcircuits.com/vol_2/chpt_1/3.html
http://www.kpsec.freeuk.com/acdc.htm

Properties of AC electrical signal

Properties of AC electrical signal :

An electrical signal is a voltage or current which conveys information, usually it means a voltage. The term can be used for any voltage or current in a circuit. 

The voltage-time graph on the right shows various properties of an electrical signal. In addition to the properties labelled on the graph, there is frequency which is the number of cycles per second.

The diagram shows a sine wave but these properties apply to any signal with a constant shape.

• Amplitude is the maximum voltage reached by the signal. It is measured in volts, V.
• Peak voltage is another name for amplitude.
• Peak-peak voltage is twice the peak voltage (amplitude). When reading an oscilloscope trace it is usual to measure peak-peak voltage.
• Time period is the time taken for the signal to complete one cycle. It is measured in seconds (s), but time periods tend to be short so milliseconds (ms) and microseconds (µs) are often used. 1ms = 0.001s and 1µs = 0.000001s.
• Frequency is the number of cycles per second. It is measured in hertz (Hz), but frequencies tend to be high so kilohertz (kHz) and megahertz (MHz) are often used. 1kHz = 1000Hz and 1MHz = 1000000Hz. 

Power Factor

Power Factor :

It is defined in several ways

(i) In alternating-current power transmission and distribution, the cosine of the phase angle between the voltage and current "cosφ".

(ii) In AC networks power factor is the ratio of resistane to impedance of the circuit ( R/Z ).

(iii) The power factor of an AC electric power system is defined as the ratio of the real power to the apparent power ( P/S ), and is a number between 0 to 1 inclusive .

Power factors other than unity have deleterious effects on power transmission systems, including excessive transmission losses and reduced system capacity.

When the load is inductive, e.g., an induction motor, the current lags the applied voltage, and the power factor is said to be a lagging power factor. When the load is capacitive, e.g., a synchronous motor or a capacitive network, the current leads the applied voltage, and the power factor is said to be a leading power  factor.Power factor equals unity (1) when the voltage and current are in phase, and is zero when the current leads or lags the voltage by 90 degrees.

Capacitive circuits cause reactive power with the current waveform leading the voltage wave by 90 degrees, while inductive circuits cause reactive power with the current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out. By convention, capacitors are said to generate reactive power while inductors are said to consume it (this probably comes from the fact that most real-life loads are inductive and so reactive power has to be supplied to them from power factor correction capacitors).

In power transmission and distribution, significant effort is made to control the reactive power flow. This is typically done automatically by switching inductors or capacitor banks in and out, by adjusting generator excitation, and by other means. Electricity retailers may use electricity meters which measure reactive power to financially penalise customers with low power factor loads. This is particularly relevant to customers operating highly inductive loads such as motors at water pumping stations. 

reference : 

http://en.wikipedia.org/wiki/Power_factor 

Synchronous Generators

Synchronous Generators

Generators are the active elements in the network.

They are connected by a shaft to turbines - in any type of power plants - to have the same speed and the same torque.

Its speed must be constant and not to vary with load variation. It can be determined by the law:

W=(120 f / P) where:

W (r.p.m) : revolution per minute.

P (poles) : number of generator poles.

f (Hz) : frequency .

· Modeling of Synchronous Generator :

The model of synchronous generator is shown in the following figure:

where :

V_t : Terminal voltage.

d : Power angle (rotor angle)

Ra : Armature resistance.

Xs : Synchronous reactance 

Xa : Armature reactance

XL : Leakage reactance.

I_a : Armature current

Cos j : Power factor.

Noting that:

1 - X_s >> R_a , (X_s / R_a > 10)

2 - X_s = X_a + X_L

3 - Emf. is always constant (neglecting any change in I_f).

4 - In some times, (R_a) is neglected w.r.t (X_s).

● Mathematical model:

The mathematical model of synchronous generator is indicated in the following equation :

 

 - Where f is the angle between the voltage and the current (the power factor angle).

reference :
http://en.wikipedia.org/wiki/Synchronous_generator

Power Plants

 Power Plants :

It is known from electrical and mechanical sciences that there are three elements: field, rotation and current, when two of them exist, the third will be produced.

To generate electrical power, the field and rotation must be exited.

The type of generation is determined according to what causes the rotation of the turbine.

Types of power plants :

1. Steam Turbine power plants.
2. Gas Turbine power plants.
3. Combined cycle steam-gas power plants.
4. Hydraulic power plants.
   
5. Nuclear power plants.

read more details :

http://en.wikipedia.org/wiki/Power_plants

Electrical Transformers

  Electrical Transformers

· Definition:

Is an electric static machine used in power system to transfer the electrical power from voltage and current level to another level.

Transformer is the main unit in the transformer stations; as it step up or down the voltage.

The network have many transformers which have different powers depends on the demand load.

-The values used for unified electrical net work for transformers are: 220kv/66kv 125MVA -75MVA.

66KV/11KV 25MVA-20MVA-12.5MVA.

· Principle Of Operation:

When the ac voltage is applied to the primary winding, a current will pass trough it producing AC magnetic flux in the iron core. This flux cuts the secondary winding which produce e.m.f across it. When the transformer is loaded , the current will pass trough the secondary winding.

Input power= output power+ power losses.

Input power= (√3) * i1* v1 * cosØ.

Output power=(√3) * i2* v2 * cosØ.

● Modeling of Transformer:

Generally, the model of power transformer is as shown in fig:

Where:

R_1, X ₁ : Resistance & reactance of primary side respectively.

R₂ , X₂: Resistance & reactance of secondary side respectively.

R_o: Iron-loss resistance, X_m: Magnetizing Reactance.

E₁: Induced emf in primary side.

E₂: Induced emf in secondary side.

Transformer is represented only by equivalent reactance = Z_eq.

  Where:

 Noting that:

1 - The ratio X/R is always >15 .

2- r_trans. can be negleted

3 - In most time X_trans. is added to X_Line (Series reactances).

4 - All represented impedance (or reactance or resistance) are

in per unit. Where:

 Z_p.u.= Z_actual / Z_base , Z_base = V²_base / S<sub>base



for more details read : 
http://en.wikipedia.org/wiki/Electrical_transformer</sub>

Impeadance Of Autotransformer

 Impeadance Of Autotransformer

The impedance of a transformer can be determined by measuring the impedance across the primary terminals with the secondary terminals short-circuited. Consider a two-winding transformer having a turns ratio n connected as a boosting autotransformer. The transformer impedance, which is mainly leakage reactance, is split between the common winding and the series winding as Zc and Zs, respectively. The magnetizing impedance is neglected. To determine the impedance of the autotransformer, the secondary (low-voltage) terminals are short-circuited and a voltage source Ep is applied to the primary (highvoltage) terminals, as shown in Figure 1.

The current through the common winding Ic is equal to the current through the series winding divided by the turns ratio:

Ic = Is/ n                                            eq 1

The voltage across the common winding Ec is equal to the voltage drop across Zc:

Ec = Ic x Zc = Is x Zc/ n                   eq 2

FIGURE 1 A boosting autotransformer with a short circuit applied at the low-voltage

output.

The voltage across the series winding Es is equal to Ec divided by the turns ratio:

Es= Ec/ n = Is x Zc /n2                                     eq  3

The current through the series winding Is is equal to the difference between the input voltage Ep and the  voltage across the series winding Es divided by Zs:

Is= (Ep - Es) / Zs                                               eq 4

Multiplying both sides of Eq. (.4) by Zs and substituting Eq. (.3) for Es:

Is x Zs =Ep - Is x Zc/n^2                             eq 5

Solving for Ep by rearranging Eq. (5):

Ep = Is x (Zs +Zc/n^2)                                      eq 6

The impedance as seen at the primary or high-voltage side of the transformer Zp is equal to Ep/Is. This is obtained by dividing both sides of Eq. (6) by Is:

Zp = Zs +( Zc/n^2)                                                eq 7

Notice that the value of Zp in Eq. (7) is equal to the series impedance as seen at the secondary or low-voltage side when the transformer is connected as a conventional two-winding transformer with the high-voltage windings short circuited. For a large ratio n this impedance is much smaller than the series impedance seen at the primary side.

In general, the series impedance of a small two-winding transformer is greater than the series impedance of a large two-winding transformer if the two impedances expressed as percent of the winding KVA bases are equal. However, when a small transformer is connected as an autotransformer the series impedance seen at the transformer terminals can be substantially smaller than the impedance of a much larger equivalent two-winding transformer. This can be quantified as follows. Let:

% ZAT = impedance of a unit connected as autotransformer expressed in percent of the winding KVA base
KVAAT = winding KVA base a unit connected as an autotransformer
% ZTW =impedance of a two-winding transformer expressed in percent of the winding KVA base
KVATW = winding KVA base of a two-winding transformer
ZAT = impedance, in ohms, of an autotransformer across the primary terminals
ZTW = impedance, in ohms, of a two-winding transformer across the primary terminals
r = ratio of the primary terminal voltage to the secondary terminal voltage 

n = turns ratio of the common/series windings of the autotransformer
Ep = primary voltage
Es = autotransformer series winding voltage
η = ratio of ZAT/ZTW

The impedance of a transformer in ohms is equal to the per unit impedance times the quantity E2 base/KVAbase. Recall from Eq. (7) that the impedance of an autotransformer seen at the primary terminals is equal to the series impedance as seen at the secondary or low-voltage side when the transformer
is connected as a conventional two-winding transformer. Therefore, Ebase = Es, and

Zat = 0.01 x %Zat x Es^2 /KVAat  ohms                              eq 8

For a two-winding transformer, Ebase = Ep, and

Ztw = 0.01 x % Ztw x(Ep^2/KVAtw)  ohms                            eq 9

The ratio ZAT/ZTW is found by dividing Eq. (8) by Eq. (9).

Zat /Ztw = (Es^2 x KVAtw x %ZAT)/(Ep^2 x KVAat x %Ztw)                        eq 10

If the two-winding transformer is replaced by an autotransformer having the same KVA capacity, the KVA rating of the autotransformer windings is smaller than the KVA rating of the two-winding transformer windings. Recalling the capacity multiplication factor of a boosting autotransformer in Eq. (1),

KVAtw/KVAat = Fc = r /r - 1                                      eq 11

For the boosting autotransformer connection, the secondary voltage is equal to the voltage across the common winding. The voltage across the series winding Es divided by the secondary voltage is therefore equal to 1/n:

Es/secondary voltage= 1/ n                                             eq 12

The ratio r was defined as the primary terminal voltage divided by the secondary terminal voltage:

Ep/secondary voltage=  r                                               eq 13

For a boosting autotransformer,

1/ n = r - 1,                                                                   eq 14

Es/Ep=(r - 1)/r                                                              eq 15

(Es/Ep)^2=(r - 1)^2/r^2                                                eq 16

Combining Eqs. (11) and (16) with Eq. (10), the following result is obtained.

η =( (r - 1) x %Zat)/(r %Ztw)                                     eq 17

Since %ZAT and %Ztw are expressed on the KVA bases of the transformer windings, the values of these values should be comparable even though the physical sizes and KVA ratings of the transformers may be very different.
For the special case where %Zat and %Ztw are equal,

η = (r - 1)/r < 1                                                           eq 18

The meaning of Eq. (18) is that the engineer has the opportunity to design an autotransformer with much lower conductor losses and regulation than would be practical with a two-winding transformer with the same KVA capacity. However, in order to limit short-circuit currents, the reactance component of the impedance must still be maintained above some minimum design limit. In Section 4.4, we will see that an autotransformer behaves very differently from a two-winding transformer when a short-circuit is applied to the output.

reference :

http://en.wikipedia.org/wiki/Autotransformer