THREE PHASE TRANSFORMER

electrical theory and electrical fundementals for all electrical related people . students , engineers, electrician #electricaltheorems,electrical,

It is the three phase system which has been adopted world over to generate, transmit and distribute electrical power. Therefore to change the level of voltages in the system three phase transformers should be used.
Three number of identical single phase transformers can be suitably connected for use in a three phase system and such a three phase transformer is called a bank of three phase transformer. Alternatively, a three phase transformer can be constructed as a single unit

In a single phase transformer, we have only two coils namely primary and secondary. Primary is energized with single phase supply and load is connected across the secondary. However, in a 3phase transformer there will be 3 numbers of primary coils and 3 numbers of secondary coils. So these 3 primary coils and the three secondary coils are to be properly connected so that the voltage level of a balanced 3-phase supply may be changed to another 3-phase balanced system of different voltage level.Suppose you take three identical transformers each of rating 10 kVA, 200 V / 100 V, 50 Hz and to distinguish them call them as A, B and C. For transformer-A, primary terminals are marked as A1A2 and the secondary terminals are marked as a1a2. The markings are done in such a way that A1 and a1 represent the dot (•) terminals. Similarly terminals for B and C transformers are marked

THREE PHASE TRANSFORMER WINDING DIAGRAM

It may be noted that individually each transformer will work following the rules of single phase transformer i.e, induced voltage in a1a2 will be in phase with applied voltage across A1A2 and the ratio of magnitude of voltages and currents will be as usual decided by a where a = N1/N2 = 2/1, the turns ratio. This will be true for transformer-B and transformer-C as well i.e., induced voltage in b1b2 will be in phase with applied voltage across BB1B2B and induced voltage in c1c2 will be in phase with applied voltage across C1C2. 

Now let us join the terminals A2, BB2 and C2 of the 3 primary coils of the transformers and no inter connections are made between the secondary coils of the transformers. Now to the free terminals A1, B1B and C1 a balanced 3-phase supply with phase sequence A-B-C is connected

. Primary is said to be connected in star.

If the line voltage of the supply is V =200*1.73 VLL, the magnitude of the voltage impressed across each of the primary coils will be 3 times less i.e., 200 V. However, the phasors 12AAV  12BBVand 12CCVwill be have a mutual phase difference of 120º Then from the fundamental principle of single phase transformer we know, secondary coil voltage 12aaVwill be parallel to 12AAV; 12bbVwill be parallel to 12BBVand 12ccVwill be parallel to 12CCV. Thus the secondary induced voltage phasors will have same magnitude i.e., 100 V but are displaced by 120º mutually. The secondary coil voltage phasors 12aaV, 12bbVand 12ccV are shown in figure 26.2. Since the secondary coils are not interconnected, the secondary voltage phasors too have been shown independent without any interconnections between them. In contrast, the terminals A2, B2 and C2 are physically joined forcing them to be equipotential which has been reflected in the primary coil voltage phasors as well where phasor points A2, B2 and C2 are also shown joined. Coming back to secondary, if a voltmeter is connected across any coil i.e., between a1 and a2 or between b1 and b2 or between c1 and c2 it will read 100 V. However, voltmeter will not read anything if connected between a1 and b1 or between b1 and c1 or between c1 and a1 as open circuit exist in the paths due to no physical connections between the coils

Imagine now the secondary coil terminals a2, b2 and c2 are joined together physically 

So the secondary coil phasors should not be shown isolated as a2, b2 and c2 become equipotential due to shorting of these terminals. Thus, the secondary coil voltage phasors should not only be parallel to the respective primary coil voltages but also a2, b2 and c2 should be equipotential. Therefore, shift and place the phasors 12aaV, 12bbVand 12ccVin such a way that they remain parallel to the respective primary coil voltages and the points a2, b2 and c2 are superposed.

Here obviously, if a voltmeter is connected between a1 and b1 or between b1 and c1 or  between c1 and a1 it will read corresponding phasor lengths a1b1 or b1 c1 or c1a1 which are all equal to 200   3V. Thus,             Va b11           ,           b c12V and    2c a1V are of same magnitude and displaced mutually by 120º to form a balanced 3-phase voltage system. Primary 3-phase line to line voltage of 200  3V is therefore stepped down to 3-phase, 100      3V line to line voltage at the secondary. The junction of A2, BB2 and C2 can be used as primary neutral and may be denoted by N. Similarly the junction of a2, b2 and c2 may be denoted by n for secondary neutral.

Star-delta connection 

To connect windings in delta, one should be careful enough to avoid dead short circuit. Suppose we want to carry out star / delta connection with the help of the above single phase transformers. HV windings are connected by shorting A2, BB2 and C2 together

As we know, in delta connection, coils are basically connected in series and from the junction points, connection is made to supply load. Suppose we connect quite arbitrarily (without paying much attention to terminal markings and polarity), a1 with b2 and b1 with c1. Should we now join a2 with c2 by closing the switch S, to complete the delta connection? As a rule, we should not join (i.e., put short circuit) between any two terminals if potential difference exists between the two. It is equivalent to put a short circuit across a voltage source resulting into very large circulating current. Therefore before closing S, we must calculate the voltage difference between a2 with c2. To do this, move the secondary voltage phasors such that a1 and b2 superpose as well as b1 with c1 superpose - this is because a1 and b2 are physically joined to make them equipotential; similarly b1 and c1 are physically joined so as to make them equipotential. The phasor diagram is

. If a voltmeter is connected across S (i.e., between a2 and c2), it is going to read the length of the phasorV. By referring to phasor 2diagram of figure 26.9, it can be easily shown that the voltage across the switch S, under this condition isV= a c o 100+ 2cos60 100 = 200V . So this connection is not proper and the switch S should not be closed.

VARIABLE FREQUENCY DRIVE (VFD)

electrical theory and electrical fundementals for all electrical related people . students , engineers, electrician #electricaltheorems,electrical,

Variable frequency drive (VFD) usage has increased dramatically in HVAC applications. The VFDs are now commonly applied to air handlers, pumps, chillers and tower fans. A better understanding of VFDs will lead to improved application and selection of both equipment and HVAC systems. This paper is intended to provide a basic understanding of common VFD terms, VFD operation, and VFD benefits. In addition this paper will discuss some basic application guidelines regarding harmonic distortion with respect to industry standards

Understanding the basic principles behind VFD operation requires understanding the three basic  sections of the VFD: the rectifier, dc bus, and inverter. The voltage on an alternating current (ac) power supply rises and falls in the pattern of a sine wave

When the voltage is positive, current flows in one direction; when the voltage is negative, the current flows in the opposite direction. This type of power system enables large amounts of energy to be efficiently transmitted over great distances. The rectifier in a VFD is used to convert incoming ac power into direct current (dc) power. One rectifier will allow power to pass through only when the  voltage is positive. A second rectifier will allow power to pass through only when the voltage is negative. Two rectifiers are required for each phase of power. Since most large power supplies are three phase, there will be a minimum of 6 rectifiers used Appropriately, the term “6 pulse” is used to describe a drive with 6 rectifiers. A VFD may have multiple rectifier sections, with 6 rectifiers per section, enabling a VFD to be “12 pulse,” “18 pulse,” or “24 pulse.” The benefit of “multipulse” VFDs will be described later in the harmonics section. Rectifiers may utilize diodes, silicon controlled rectifiers 

microprocessor to control when the power may begin to flow, making this type of rectifier useful for solid-state starters as well. Transistors include a gate circuit that enables a microprocessor to open or close at any time, making the transistor the most close at any time, making the transistor the most close at any time, making the transistor the most close at any time, making the transistor the most close at any time, making the transistor the most useful device of the three. A VFD using transistors in the rectifier section is said to have an “active front end.” After the power flows through the rectifiers it is stored on a dc bus. The dc bus contains capacitors to accept power from the rectifier, store it, and later deliver that power through the inverter section. The dc bus may also contain inductors, dc links, chokes, or similar items that add inductance, thereby smoothing the incoming power supply to the dc bus. smoothing the incoming power supply to the dc bus. The final section of the VFD is referred to as an “inverter.” 

The inverter contains transistors that deliver power to the motor. The “Insulated Gate Bipolar Transistor” (IGBT) is a common choice in modern VFDs. The IGBT can switch on and off several thousand times per second and precisely control the power delivered to the motor. The IGBT uses a method named “pulse width modulation” (PWM) to simulate a current sine wave at the desired frequency to the motor. Motor speed (rpm) is dependent upon frequency. Varying the frequency output of the VFD controls

motor speed: Speed (rpm) = frequency (hertz) x 120 / no. of poles

SPEED CONTROL OF DC SHUNT MOTOR

electrical theory and electrical fundementals for all electrical related people . students , engineers, electrician #electricaltheorems,electrical,

We know that the speed of shunt motor is given by:

where, Va is the voltage applied across the armature and φ is the flux per pole and is proportional to the field current If. As explained earlier, armature current Ia is decided by the mechanical load present on the shaft. Therefore, by varying Va and If we can vary n. For fixed supply voltage and the motor connected as shunt we can vary Va by controlling an external resistance connected in series with the armature. If of course can be varied by controlling external field resistance Rf connected with the field circuit. Thus for .shunt motor we have essentially two methods for controlling speed, namely by:

1. varying armature resistance.

2. varying field resistance.

Speed control by varying armature resistance 

The inherent armature resistance r_a being small, speed n versus armature current I_a characteristic will be a straight line with a small negative slope  In the discussion to follow we shall not disturb the field current from its rated value. At no load (i.e., I_a = 0) speed is highest and Note that for shunt motor voltage applied to the field and armature circuit are same and equal to the supply voltage V. However, as the motor is loaded, I_ar_a drop increases making speed a little less than the no load speed n₀. For a well designed shunt motor this drop in speed is small and about 3 to 5% with respect to no load speed. This drop in speed from no load to full load condition expressed as a percentage of no load speed is called the inherent speed regulation of the motor.

It is for this reason, a d.c shunt motor is said to be practically a constant speed motor (with no external armature resistance connected) since speed drops by a small amount from no load to full load condition.

Since eT=kI φ, for constant φ operation, Te becomes simply proportional to Ia. Therefore, speed vs. torque characteristic is also similar to speed vs. armature current characteristic

The slope of the n vs Ia or n vs Te characteristic can be modified by deliberately connecting external resistance rext in the armature circuit. One can get a family of speed vs. armature curves for various values of rext. From these characteristic it can be explained how speed control is achieved. Let us assume that the load torque TL is constant and field current is also kept constant. Therefore, since steady state operation demands Te = TL, Te = akIφ too will remain constant; which means Ia will not change. Suppose rext = 0, then at rated load torque, operating point will be at C and motor speed will be n. If additional resistance rext1 is introduced in the armature circuit, new steady state operating speed will be n1 corresponding to the operating point D. In this way one can get a speed of n2 corresponding to the operating point E, when rext2 is introduced in the armature circuit. This same load torque is supplied at various speed. Variation of the speed is smooth and speed will decrease smoothly if rext is increased. Obviously, this method is suitable for controlling speed below the base speed and for supplying constant rated load torque which ensures rated armature current always. Although, this method provides smooth wide range speed control (from base speed down to zero speed), has a serious draw back since energy loss takes place in the external resistance rext reducing the efficiency of the motor

Speed control by varying field current

In this method field circuit resistance is varied to control the speed of a d.c shunt motor. Let us rewrite .the basic equation to understand the method

If we vary I_f, flux φ will change, hence speed will vary. To change I_f an external resistance is connected in series with the field windings. The field coil produces rated flux when no external resistance is connected and rated voltage is applied across field coil. It should be understood that we can only decrease flux from its rated value by adding external resistance. Thus the speed of the motor will rise as we decrease the field current and speed control above the base speed will be achieved. Speed versus armature current characteristic  for two flux values φ and 1φ. Since 1<φφ, the no load speed 'on for flux value 1φ is more than the no load speed n_o corresponding to φ. However, this method will not be suitable for constant load torque.

To make this point clear, let us assume that the load torque is constant at rated value So from the initial steady condition, we have 1=L ratedea ratedT=TkIφ. If load torque remains constant and flux is reduced to 1φ, new armature current in the steady state is obtained from 11aL ratekI=T φ. Therefore new armature current is

 

But the fraction,1 1>φφ; hence new armature current will be greater than the rated armature current and the motor will be overloaded. This method therefore, will be suitable for a load whose torque demand decreases with the rise in speed keeping the output power constant  Obviously this method is based on flux weakening of the main field. Therefore at higher speed main flux may become so weakened, that armature reaction effect will be more pronounced causing problem in commutation

Speed control by armature voltage variation

In this method of speed control, armature is supplied from a separate variable d.c  voltage source, while the field is separately excited with fixed rated voltage . Here the armature resistance and field current are not varied. Since the no load speed  N  0=Va/knφ,  the speed versus Ia characteristic will shift parallely for different values of Va. As flux remains constant, this method is suitable for constant torque loads. In a way armature voltage control method is similar to that of armature resistance control method except that the former one is much superior as no extra power loss takes place in the armature circuit. Armature voltage control method is adopted for controlling speed from base speed down to very small speed as one should not apply across the armature a voltage which is higher than the rated voltage. 

Ward Leonard method: combination of V_a and I_f control 

In this scheme, both field and armature control are integrated Arrangement for field control is rather simple. One has to simply connect an appropriate rheostat in the field circuit for this purpose. However, in the pre power electronic era, obtaining a variable d.c supply was not easy and a separately excited d.c generator was used to supply the motor armature. Obviously to run this generator, a prime mover is required. A 3-phase induction motor is used as the prime mover which is supplied from a 3-phase supply. By controlling thefield current of the generator, the generated emf, hence Va can be varied. The potential divider connection uses two rheostats in parallel to facilitate reversal of generator field current 

First the induction motor is started with generator field current zero (by adjusting the jockey positions of the rheostats). Field supply of the motor is switched on with motor field rheostat set to zero. The applied voltage to the motor Va, can now be gradually increased to the rated value by slowly increasing the generator field current. In this scheme, no starter is required for the d.c motor as the applied voltage to the armature is gradually increased. To control the speed of the d.c motor below base speed by armature voltage, excitation of the d.c generator is varied, while to control the speed above base speed field current of the d.c motor is varied maintaining constant Va. Reversal of direction of rotation of the motor can be obtained by adjusting jockeys of the generator field rheostats. Although, wide range smooth speed control is achieved, the cost involved is rather high as we require one additional d.c generator and a 3-phase induction motor of simialr rating as that of the d.c motor whose  speed is intended to be controlled.  

POWER FACTOR

electrical theory and electrical fundementals for all electrical related people . students , engineers, electrician #electricaltheorems,electrical,

Power factor is simply a name given to the ratio of “actual” power (active power) being used in a circuit, expressed in watts or more commonly kilowatts (kW), to the power which is “apparently” being drawn from the mains, expressed in volt-ampere or more commonly kilo volt-ampere (kVA).

All modern industries utilize electrical energy in some form or other. Two basic categories of load are encountered in alternate current (AC) networks.

1.  Resistive Loads

Devices containing only resistance e.g. incandescent lamps, heaters, soldering irons, ovens, etc.

The current drawn from the supply is directly converted into heat or light.  Since the voltage is assumed to be constant, the actual power (kW) being used is identical to the apparent power (kVA) being drawn from the line.  The power factor is therefore unity or 1.  In these purely resistive circuits, the current and voltage sinewave peaks occur simultaneously and are said to be “in phase”.

2.  Inductive Loads 

All motors and transformers depend on magnetism as the basis of

their operation.  Magnetism is a force and in the physical sense is not

consumed.  In AC motors and transformers, magnetic forces are only

required periodically.  Consequently, a permanent magnet cannot be

used and the necessary magnetism is produced by electrical means.

The electrical current needed for this purpose is not fully utilised.

Having produced the magnetic force, the current flows back to the

power station again.  This current is called the reactive current in con-

trast to the active current which performs work and is fully utilised in

so doing.  Although the reactive current is not utilised, it imposes a

load on the electrical distribution system and supply authorities

demand payment for this load according to specific tariffs.

The current drawn from the supply is made up of two separate kinds

of current “power producing current”  and “magnetising current”.

Therefore the current flowing in an AC circuit (unless corrected) is

generally larger than is necessary to supply the power being by the

expended point.

What does Cosϕ mean?

Reactive power and active power flow through the motor or trans-

former.  Geometrical calculation of these two powers yield the apparent power.  The ratio of the active and apparent power is denoted by cosϕ and indicates what fraction of apparent power flowing is actually used by the motor.The apparent power is greater than theactive power and hence the power factor is a value considerably lessthan unity.

Disadvantages of Low Power Factor

1.    Increased authorities cost since more current has to be transmitted, and this cost is directly billed to consumers on maximum demand kVA systems.

2.      Causes overloaded generators, transformers and distribution lines within a plant, resulting in greater voltage drops and power losses, all representing waste, inefficiency and needless wear and tear on industrial  electrical equipment

3.    Reduces load handling capability of the plants electrical system.Most electrical supply authorities have changed to kVA demand systems from the inefficient kW demand system.  Consumers are now billed and penalised for their inefficient systems according to the apparent power being used.  In future, consumers will be penalised for plants with power factor below a pre-determined value.

Power Factor Improvement

The term power factor comes into picture in AC circuits only. Mathematically it is cosine of the phase difference between source voltage and current. It refers to the fraction of total power (apparent power) which is utilized to do the useful work called active power.

Need for Power Factor Improvement

• Real power is given by P = VIcosφ. To transfer a given amount of power at certain voltage, the electrical current is inversely proportional to cosφ. Hence higher the pf lower will be the current flowing. A small current flow requires less cross sectional area of conductor and thus it saves conductor and money.

• From above relation we saw having poor power factor increases the current flowing in conductor and thus copper loss increases. Further large voltage drop occurs in alternator,electrical transformer and transmission & distribution lines which gives very poor voltage regulation

How to calculate the capacitor for motor

Qc  =0.9x1.73xUnI0        

Un  is motor voltage

I0  is no load current of induction motor