# ELECTRICAL MACHINES 2 BY GNANAVADIVEL PDF

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Conditions required for paralleling A diagram shows that Generator 2 oncoming generator will be connected in parallel when the switch S1 is closed. However, closing the switch at an arbitrary moment can severely damage both generators! If voltages are not exactly the same in both lines i.

Therefore, to avoid this, voltages coming from both generators must be exactly the same. Therefore, the following conditions must be met: The phase angles of two a phases must be equal.

The frequency of the oncoming generator must be slightly higher than the frequency of the running system. Conditions required for paralleling If the phase sequences are different, then even if one pair of voltages phases a are in phase, the other two pairs will be out of phase creating huge currents in these phases. If the frequencies of the generators are different, a large power transient may occur until the generators stabilize at a common frequency.

The frequencies of two machines must be very close to each other but not exactly equal. If frequencies differ by a small amount, the phase angles of the oncoming generator will change slowly with respect to the phase angles of the running system.

If the angles between the voltages can be observed, it is possible to close the switch S1 when the machines are in phase. General procedure for paralleling generators When connecting the generator G2 to the running system, the following steps should be taken: Adjust the field current of the oncoming generator to make its terminal voltage equal to the line voltage of the system use a voltmeter.

Compare the phase sequences of the oncoming generator and the running system. This can be done by different ways: If the motor rotates in the same direction, the phase sequence is the same; 2 Connect three light bulbs across the open terminals of the switch. As the phase changes between the two generators, light bulbs get brighter large phase difference or dimmer small phase difference.

If all three bulbs get bright and dark together, both generators have the same phase sequences. General procedure for paralleling generators If phase sequences are different, two of the conductors on the oncoming generator must be reversed. The frequency of the oncoming generator is adjusted to be slightly higher than the systems frequency. Turn on the switch connecting G2 to the system when phase angles are equal.

The simplest way to determine the moment when two generators are in phase is by observing the same three light bulbs. When all three lights go out, the voltage across them is zero and, therefore, machines are in phase. A more accurate way is to use a synchroscope a meter measuring the difference in phase angles between two a phases.

However, a synchroscope does not check the phase sequence since it only measures the phase difference in one phase. The whole process is usually automated.

Concept of the infinite bus When a synchronous generator is connected to a power system, the power system is often so large that nothing, the operator of the generator does, will have much of an effect on the power system. An example of this situation is the connection of a single generator to the power grid. Our power grid is so large that no reasonable action on the part of one generator can cause an observable change in overall grid frequency.

This idea is idealized in the concept of an infinite bus. An infinite bus is a power system so large that its voltage and frequency do not vary regardless of how much real or reactive power is drawn from or supplied to it. The real and reactive power delivered by a synchronous generator or consumed by a synchronous motor can be expressed in terms of the terminal voltage Vt, generated voltage Ef, synchronous impedance Zs, and the power angle or torque angle.

Referring to Fig.

The generator action corresponds to positive value of , while the motor action corresponds to negative value of. The above two equations for active and reactive powers hold good for cylindrical-rotor synchronous machines for negligible resistance To obtain the total power for a three-phase generator, the above equations should be multiplied by 3 when the voltages are line-toneutral If the line-to-line magnitudes are used for the voltages, however, these equations give the total three-phase power.

Steady-state power-angle or torque-angle characteristic of a cylindrical-rotor synchronous machine with negligible armature resistance. Real power or torque Pull-out torque as a generator. The above equation shows that the power produced by a synchronous generator depends on the angle between the Vt and Ef.

The maximum power indicated by this equation is called steady-state stability limit of the generator. If we try to exceed this limit such as by admitting more steam to the turbine , the rotor will accelerate and lose synchronism with the infinite bus. In practice, this condition is never reached because the circuit breakers trip as soon as synchronism is lost. We have to resynchronize the generator before it can again pick up the load.

Normally, real generators never even come close to the limit. Full-load torque angle of 15o to 20o are more typical of real machines. However, in a salient-pole machine, the two mmfs do not act on the same magnetic circuit.

The direct axis component Fad operates over a magnetic circuit identical with that of the field system, while the q-axis component Faq is applied across the interpole space, producing a flux distribution different from that of Fad or the Field mmf. The Blondel's two reaction theory hence considers the results of the cross and directreaction components separately and if saturation is neglected, accounts for their different effects by assigning to each an appropriate value for armature-reaction "reactive" respectively Xaq and Xad.

Let lq and Id be the q and d-axis components of the current I in the armature reference to the phasor diagram in Figure. We get the following relationships. Short Circuit Phenomenon Consider a two pole elementary single phase alternator with concentrated stator winding as shown in Fig. Consider a two pole elementary single phase alternator with concentrated stator winding as shown in Fig. Let short circuit occurs at position of rotor shown in Fig. The stator opposes this by a current in the shown direction as to force the flux in the leakage path.

The rotor current must increase to maintain its flux constant. It reduces to normal at position c where stator current is again reduces to zero. The waveform of stator current and field current shown in the Fig. Thus the short circuit current is a function of relative position of stator and rotor.

Using the theorem of constant linkages a three phase short circuit can also be studied. After the instant of short circuit the flux linking with the stator will not change. A stationary image of main pole flux is produced in the stator.

Thus a d. The magnitude of d. The rotor tries to maintain its own poles.

The rotor current is normal each time when rotor poles occupy the position same as that during short circuit and the current in the stator will be zero if the machine is previously unloaded. After one half cycle from this position the stator and rotor poles are again coincident but the poles are opposite. To maintain the flux linkages constant, the current in rotor reaches to its peak value. The stationary field produced by poles on the stator induces a normal frequency emf in the rotor.

Thus the rotor current is fluctuating whose resultant a.

Thus the waveform of transient current consists of fundamental, a. Thus whenever short circuit occurs in three phase generator then the stator currents are distorted from pure sine wave and are similar to those obtained when an alternating voltage is suddenly applied to series R-L circuit. If a generator having negligible resistance, excited and running on no load is suddenly undergoing short circuit at its terminals, then the emf induced in the stator winding is used to circulate short circuit current through it.

Initially the reactance to be taken into consideration is not the synchronous reactance of the machine. The effect of armature flux reaction is to reduce the main field flux. But the flux linking with stator and rotor can not change instantaneously because of the induction associated with the windings. Thus at the short circuit instant, the armature reaction is ineffective.

It will not reduce the main flux. Thus the synchronous reactance will not come into picture at the moment of short circuit. The only limiting factor for short circuit current at this instant is the leakage reactance.

After some time from the instant of short circuit, the armature reaction slowly shows its effect and the alternator then reaches to steady state. Thus the short circuit current reaches to high value for some time and then settles to steady value.

It can be seen that during the initial instant of short circuit is dependent on induced emf and leakage reactance which is similar to the case which we have considered previously of voltage source suddenly applied to series R-L circuit. The instant in the cycle at which short occurs also affects the short circuit current.

Near zero e. The expressions that we have derived are applicable only during initial conditions of short circuit as the induced emf also reduces after some tome because of increased armature reaction.

The short circuit currents in the three phases during short circuit are as shown in the Fig next slide. The rating of synchronous generators is specified in terms of maximum apparent power in KVA and MVA load at a specified power factor normally 80, 85 or 90 percent lagging and voltage for which they are designed to operate under steady state conditions.

This load is carried by the alternators continuously without overheating. The power factor is also important factor that must be specified. This is because the alternator that is designed to operate at 0. More field current results in overheating of the field system which is undesirable. For this compounding curves of the alternators can be drawn. If synchronous generator is supplying power at constant frequency to a load whose power factor is constant then curve showing variation of field current versus armature current when constant power factor load is varied is called compounding curve for alternator.

To maintain the terminal voltage constant the lagging power factors require more field excitation that that required for leading power factors. Hence there is limitation on output given by exciter and current flowing in field coils because of lagging power factors. The ability of prime mover decides the active power output of the alternator which is limited to a value within the apparent power rating.

The capability curve for synchronous generator specifies the bounds within which it can operate safely. The loading on generator should not exceed the generator rating as it may lead to heating of stator.

The turbine rating is the limiting factor for MW loading. The field current should not exceed its limiting value as it may cause rotor heating. All these considerations provides performance curves which are important in practical applications.

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A set of capability curves for an alternator is shown in Fig. The effect of increased Hydrogen pressure is shown which increases the cooling. When the active power and voltage are fixed the allowable reactive power loading is limited by either armature or field winding heating. From the capability curve shown in Fig. From unity p. This fact can be derived as follows:. If the alternator is operating is constant terminal voltage and armature current which the limiting value corresponding to heating then the operation of alternator is at constant value of apparent power as the apparent power is product of terminal voltage and current, both of which are constant.

If P is per unit active power and Q is per unit reactive power then per unit apparent power is given by,. Similarly, considering the alternator to be operating at constant terminal voltage and field current hence E is limited to a maximum value obtained by heating limits.

Thus induced voltage E is given by, If Ra is assumed to be zero then The apparent power can be written as, Substituting value of a obtained from 1 in equation 2 , Taking magnitudes,. These two circles are represents in the Fig. The field heating and armature heating limitation on machine operation can be seen from this Fig. The rating of machine which consists of apparent power and power factor is specified as the point of intersection of these circles as shown in the Fig. So that the machine operates safely.

Rated between kW to 15MW with speeds ranging from to rpm. Constant speed motor. When 3 phase supply is given to the stator winding, 3 phase current flows which produces 3 phase flux The MMF wave of the stator will have rotating effect on the rotor The effect of the field will be equal to that produced by a rotating pole. Looking back at the waveform again, we see that at any instant, one waveform has zero magnitude and one has a positive value and the other, negative value Let us consider at the following instances 0, 60, , degrees.

We have a rotating field at the stator Rotor is another magnet If properly aligned?! It is true that magnetic locking will make the rotor run at synchronous speed Locking cannot happen instantly in a machine?

This makes synchronous motors not self starting. If the rotor is moved by external means to overcome inertial force acting on it then there is a chance for the motor to get started. We call it as back emf Similar to generated emf in an alternator Rotor rotating at synchronous speed will induce emf in the stationary armature conductors The ac voltage applied has to overcome this back emf to circulate current through the armature winding.

The speed of the Synchronous motor speed stays constant at synchronous speed even when the load is increased Magnetic locking between the stator and rotor stiffness of coupling keeps the rotor run at synchronous speed But when the angle of separation is 90, then stiffness locking is lost and the motor ceases to run.

In all the cases discussed above, magnitude of current vector changes Power factor changes But the product Icos would be constant so that active power drawn by the machine remains constant.

The resultant air gap flux is due to ac armature winding and dc field winding If the field is sufficient enough to set up the constant air gap flux then the magnetizing armature current required from the ac source is zero hence the machine operates at unity power factor this field current is the normal field current or normal excitation.

If the field current is less than the normal excitation then the machine is under excited This deficiency in flux must be made by the armature mmf so the armature winding draws magnetizing current or lagging reactive MVA leaving the machine to operate at lagging power factor. In case the field current is made more than its normal operation then the machine is over excited This excess flux must be neutralized by the armature mmf so the machine draws demagnetizing current or leading reactive MVA leaving the machine to operate at leading power factor.

This feature of synchronous motor makes it suitable for improving the power factor of the system Motors are overexcited so that it draws leading current from the supply The motor here is referred to as synchronous condenser.

Excitation Circle diagram It gives the locus of armature current, as the excitation voltage and load angle are varied. Each component in the above expression is a current component It can be taken in such a way that they lag from their corresponding voltage component by power factor angle.

This again gives the locus of armature current, as the mechanical power developed and power factor is varied. We know, excitation circle diagram shows locus of armature current as a function of excitation voltage Power circle diagram shows locus of armature current as a function of power When these two circles are super imposed. Operation of infinite bus bars Presented by C. Operation of AC Generators in Parallel with Large Power Systems Isolated synchronous generator supplying its own load is very rare emergency generators In general applications more than one generator operating in parallel to supply loads In Iran national grid hundreds of generators share the load on the system Advantages of generators operating in parallel: When a Syn.

Iran grid , no reasonable action on part of one generator can cause an observable change in overall grid frequency This idea belong to definition of Infinite Bus which is: Operation of AC Generators in Parallel with Large Power Systems Assume generator just been paralleled with infinite bus, generator will be floating on the line, supplying a small amount of real power and little or no reactive power Suppose generator paralleled, however its frequency being slightly lower than systems operating frequency At this frequency power supplied by generator is less than systems operating frequency, generator will consume energy and runs as motor.

Operation of AC Generators in Parallel with Large Power Systems In order that a generator comes on line and supply power instead of consuming it, we should ensure that oncoming machines frequency is adjusted higher than running systems frequency Many generators have reverse-power trip system And if such a generator ever starts to consume power it will be automatically disconnected from line. As seen earlier, synchronous motor is not self starting. It is necessary to rotate the rotor at a speed very near to synchronous speed.

This is possible by various method in practice. The various methods to start the synchronous motor are, 1. Using pony motors 2. Using damper winding 3. As a slip ring induction motor 4. Using small d. Using pony motors In this method, the rotor is brought to the synchronous speed with the help of some external device like small induction motor. Such an external device is called 'pony motor'. Once the rotor attains the synchronous speed, the d.

Once the synchronism is established pony motor is decoupled. The motor then continues to rotate as synchronous motor. Using Small D. Machine Many a times, a large synchronous motor are provided with a coupled d. This machine is used as a d. Then the excitation to the rotor is provided.

Once motor starts running as a synchronous motor, the same d. The field of the synchronous motor is then excited by this exciter itself. Current loci for constant power input, constant excitation and constant power developed Refer Book for detail study.

Synchronous motors are not self starting machines. These machines are made self starting by providing a special winding in the rotor poles, known as damper winding or squirrel cage windings.

## [PDF] Electrical Machines- III By U.A.Bakshi, M.V.Bakshi Book Free Download

The damper winding consists of short circuited copper bars embedded in the face of the rotor poles When an ac supply is provided to stator of a 3-phase synchronous motor, stator winding produces rotating magnetic field. Due to the damper winding present in the rotor winding of the synchronous motor, machine starts as induction motor Induction machine works on the principle of induction. Damper windings in synchronous motor will carryout the same task of induction motor rotor windings.

Therefore due to damper windings synchronous motor starts as induction motor and continue to accelerate. The exciter for synchronous motor moves along with rotor. Functions of Damper Windings: Damper windings helps the synchronous motor to start on its own self starting machine by providing starting torque By providing damper windings in the rotor of synchronous motor "Hunting of machine can be suppressed. When there is change in load, excitation or change in other conditions of the systems rotor of the synchronous motor will oscillate to and fro about an equilibrium position.

At times these oscillations becomes more violent and resulting in loss of synchronism of the motor and comes to halt.

## Electrical Machines - II Book by M. V. BAKSHI, U. A. BAKSHI

When synchronous motor is over excited it takes leading p. And motor runs with almost zero leading power factor condition. This characteristics is similar to a normal capacitor which takes leading power factor current. Hence over excited synchronous motor operating on no load condition is called as synchronous condenser or synchronous capacitor.

This is the property due to which synchronous motor is used as a phase advancer or as power improvement device.

Disadvantage of Low Power Factor. In various industries, many machines are of induction motor type. The lighting and heating loads are supplied through transformers. The induction motors and transformers draw lagging current from the supply. Hence the overall power factor is very low and lagging in nature. The high current due to low p. For higher current, conductor size required is more which increases the cost.

The p. This increases the cost.

## Electrical Machines - II

Large current means more copper losses and poor efficiency. Large current causes large voltage drops in transmission lines, alternators and other equipments.

This results into poor regulation. Principle of Operation Presented by C. Core loss 2. No load current I0 4. Ic, Rc, I, Xm 6. Mechanical faults, noise. Rated per voltage V0, with rated freq is given to stator. Vary input voltage and note input power Input Power.

The equivalent ckt. Draw x and y axes V1 on y axis Line I0Isc is 2. Draw parallel line to x axis from I0. This line indicates constant loss vertically. Draw circle with C as a centre 7. Draw perpendicular from Isc on x axis.. Divide IscL1 in such a way that. T L1 r1 Stator Cu Loss. Join I0T. This is called as Torque Line. P is operating point Join O and P.

Cos1 is operating pf. Determine the following 1. Max Power and Max Torque are not occurring at same time Contradiction to max power transfer theorem. Separation of Losses Presented by C. Step by step reduce the voltage till the machine slip suddenly start to increase and the motor tends to rest stall. The core loss decrease almost square of the voltage and windage and friction loss remains almost constant. Formulae for calculating the equivalent circuit parameters: The outer cage alloy in the rotor has high resistance and low reactance which is used for starting purpose.

The inner cage copper has a low resistance and high reactance which is used for running purpose. The constructional arrangement and torque-speed characteristics as shown in fig.

High starting torque. Low I2R loss under running conditions and high efficiency. Principle of operation Induction generators and motors produce electrical power when their rotor is rotated faster than the synchronous speed. For a fourpole motor operating on a 50 Hz will have synchronous speed equal to rpm. In normal motor operation, stator flux rotation is faster than the rotor rotation. This is causing stator flux to induce rotor currents, which create rotor flux with magnetic polarity opposite to stator.

In this way, rotor is dragged along behind stator flux, by value equal to slip. In generator operation, a prime mover turbine, engine is driving the rotor above the synchronous speed. Stator flux still induces currents in the rotor, but since the opposing rotor flux is now cutting the stator coils, active current is produced in stator coils and motor is now operating as a generator and sending power back to the electrical grid.

This is possible only if the machine is mechanically driven above the synchronous speed. The torque-slip curve is shown in fig. Torque will become zero at synchronous speed. If the speed increases above the synchronous speed, the slip will be negative. Induction generator differs from the synchronous generator as Dc current excitation is not required. Synchronisation is not required. It does not hunt or drop out of synchronism Simple in construction Cheaper in cost Easy maintenance Induction regulators provide a constant voltage adjustment depending on the loading of the lines.

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Numerical Methods:Four different speeds can be obtained 1. Excitation Circle Diagram contd. First edition. Dynamic braking requires less power. Stator is a hollow cylinder whose inner periphery houses armature conductors Winding is excited with single phase supply.

Voltage is changed by transformer action and not by dropping voltage as that of reactor 2. Frequency of Induced EMF Every time a complete pair of poles crosses the conductor, the induced voltage goes through one complete cycle.

Calculation can be based on the equivalent circuit of Fig. The frequency of the oncoming generator must be slightly higher than the frequency of the running system.

Therefore, the following conditions must be met: