Intorduction to Power Engineering - 4 Generators

8/12/2019 Intorduction to Power Engineering - 4 Generators

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Dr Houssem Rafik El Hana Bouchekara 1

Introduction To Power

Engineering

Dr : Houssem Rafik El HanaBOUCHEKARA

2010/2011 1431/1432

KINGDOM OF SAUDI ARABIAMinistry Of High Education

Umm Al-Qura UniversityCollege of Engineering & Islamic Architecture

Department Of Electrical Engineering


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4 GENERATORS ................................................................................................................ 3

4.1 THE SIMPLE GENERATOR ........................................................................................... 3 4.2 MAIN GENERATOR TYPES .................................................................................................. 4

4.2.1 Cooling ................................................................................................................... 8 4.3 THE SYNCHRONOUSMACHINE: PRELIMINARIES ......................................... ........................... 9 4.4 P-POLEMACHINES ....................................................................................................... 10 4.5 SYNCHRONOUSMACHINEFIELDS ..................................................................................... 12 4.6 A SIMPLEEQUIVALENTCIRCUIT ...................................................................... ................. 14 4.7 PRINCIPALSTEADY-STATE CHARACTERISTICS ............................................. ......................... 16 4.8 POWER-ANGLECHARACTERISTICSAND THE INFINITEBUS CONCEPT ....................................... 18

4.8.1 Reactive Power Generation ................................................................ ................. 21


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4 G ENERATORS

The synchronous machine as an ac generator, driven by a turbine to convertmechanical energy into electrical energy, is the major electric power generating sourcethroughout the world.

The backbone of any electric power system is a number of generating stationsoperating in parallel. At each station there may be several synchronous generators operatingin parallel. Synchronous machines represent the largest single-unit electric machine inproduction. Generators with power ratings of several hundred to over a thousandmegavoltamperes (MVA) are fairly common in many utility systems. A synchronous machineprovides a reliable and efficient means for energy conversion.

The operation of a synchronous generator is (like all other electromechanical energyconversion devices) based on Faradays law of electromagnetic induction. The termsynchronous refers to the fact that this type of machine operates at constant speed andfrequency under steady-state conditions. Synchronous machines are equally capable ofoperating as motors, in which case the electric energy supplied at the armature terminals ofthe unit is converted into mechanical form.

4.1 THE SIMPLE GENERATOR

For the purpose of developing a conceptual understanding of the generator, let usbegin by considering a greatly simplified setup that includes only a single wire and a barmagnet. The objective is to induce a current in the wire; in a real generator, this wirecorresponds to the armature, or the conductors that are electrically connected to the load.This can be accomplished by moving the wire relative to the magnet, or the magnet relativeto the wire, so that the magnetic field at the location of the wire increases, decreases, orchanges direction. In order to maximize the wires exposure to the magnet, since the fielddecreases rapidly with distance, we form a loop of wire that surrounds the bar (with justenough space in between).

Figure 1: Figure The simple generator.

Now we can produce an ongoing relative motion by rotation: either we rotate themagnet inside the loop, or we hold the magnet fixed and rotate the loop around it.


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4.2 M AIN GENERATOR TYPES

The two main types of generator are turbo or cylindrical-rotor and salient-polegenerators. Both these types are synchronous machines in which the rotor turns in exactsynchronism with the rotating magnetic field in the stator.

The largest generators used in major power stations are usually turbo-generators.They operate at high speeds and are usually directly coupled to a steam or gas turbine.

The general construction of a turbo-generator is shown in Figure 2. The rotor ismade from solid steel for strength, and embedded in slots within the rotor are the field orexcitation windings. The outer stator also contains windings which are located in slots, this isagain for mechanical strength and so that the teeth between the slots form a good magneticpath. Most of the constructional features are very specialized, such as hydrogen coolinginstead of air, and direct water cooling inside the stator windings, so only passing referenceis made to this class of machines in the following descriptions.

More commonly used in smaller and medium power ranges is the salient-polegenerator. An example is shown in Figure 3. Here, the rotor windings are wound around thepoles which project from the centre of the rotor. The stator construction is similar in form tothe turbo-generator stator shown in Figure 2.

Less commonly used are induction generators and inductor alternators. Inductiongenerators have a simple form of rotor construction as shown in Figure 4, in whichaluminium bars are cast into a stack of laminations. These aluminium bars require noinsulation and the rotor is therefore much cheaper to manufacture and much more reliablethan the generators shown in Figure 2 and Figure 3. The machine has characteristics whichsuit wind turbines very well, and they also provide a low-cost alternative for small portablegenerators.

Inductor alternators have laminated rotors with slots, producing a flux pulsation inthe stator as the rotor turns. These machines are usually used for specialized applicationsrequiring high frequency.


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(a)

(b)


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(c)

Figure 2: Turbo-generator construction: (a) stator (b) rotor (c) assembly (courtesy of ABB ALSTOM Power)

(a)


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(b)

(c)

Figure 3: Salient-pole generator construction: Top: stator, Bottom: rotor (courtesy of Generac Corporation)


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Figure 4: Induction generator construction (courtesy of Invensys Brook Crompton)

4.2.1 C OOLING

Adequate cooling is a vital part of the design and performance of a generator.Forced cooling is needed because of the high loss densities that are necessary to makeeconomic use of the magnetic and electrical materials in the generator.

The most critical areas in the machine are the windings, and particularly the rotorwinding. It is explained in section 3.3 that the life expectancy of an insulation systemdecreases rapidly if its operating temperature exceeds recommended temperatures. It iscrucial for reliability therefore that the cooling system is designed to maintain the windingtemperatures within these recommended limits. As shown in Table 3.4, insulation materialsand systems are defined by a series of letters according to their temperature capability. As

improved insulation with higher temperature capability has become available, this has beenadopted in generator windings and so the usual class of insulation has progressed from classA (40 50 years ago) through class E and class B to class F and class H, the latter two beingthe systems generally in use at present.

Class H materials are available and proven, and this system is becoming increasinglyaccepted. An important part of the generator testing process is to ensure that the coolingsystem maintains the winding temperature within specified limits, and this is explained laterin section 5.8.

In turbogenerators it has already been noted that very complex systems using

hydrogen and de-ionized water within the stator coils are used. The cooling of small andmedium-sized machines is achieved by a flow of air driven around the machine by a rotor-


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mounted fan. A typical arrangement is shown in Fig. 5.18. In this case the cooling air isdrawn in through ducts; it is then drawn through the air gap of the machine and ductsaround the back of the stator core before reaching the centrifugal fan which then expels theair from the machine. There are many variations to the cooling system, particularly for largergenerators. In some machines there is a closed circulated air path cooled by a secondaryheat exchanger which rejects the heat to the outside atmosphere. This results in a large andoften rectangular generator enclosure as shown in Figure 5.

Figure 5: Closed air circuit cooled generator (courtesy of Brush Electrical Machines)

4.3 T HE S YNCHRONOUS M ACHINE : P RELIMINARIES

The armature winding of a synchronous machine is on the stator, and the field

winding is on the rotor as shown in Figure 6. The field is excited by the direct current that isconducted through carbon brushes bearing on slip (or collector) rings. The dc source is calledthe exciter and is often mounted on the same shaft as the synchronous machine. Variousexcitation systems with ac exciters and solid-state rectifiers are used with large turbinegenerators. The main advantages of these systems include the elimination of cooling andmaintenance problems associated with slip rings, commutators, and brushes.

The pole faces are shaped such that the radial distribution of the air-gap flux densityB is approximately sinusoidal as shown in Figure 7. The armature winding will include manycoils. One coil is shown in Figure 6 and has two coil sides (a and a) placed in diametrically

opposite slots on the inner periphery of the stator with conductors parallel to the shaft ofthe machine. The rotor is turned at a constant speed by a power mover connected to its


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shaft. As a result, the flux waveform sweeps by the coil sides a and a. The induced voltagein the coil is a sinusoidal time function. For each revolution of the two poles, the coil voltagepasses through a complete cycle of values. The frequency of the voltage in cycles per second(hertz) is the same as the rotor speed in revolutions per second. Thus, a two-polesynchronous machine must revolve at 3600 r/min to produce a 60-Hz voltage.

Figure 6: Simplified Sketch of a Synchronous Machine.

Figure 7: Space Distribution of Flux Density in a Synchronous Generator.

Figure 8: A Cylindrical Rotor Two-Pole Machine.

4.4 P -P OLE M ACHINES

Many synchronous machines have more than two poles. A P-pole machine is onewith P poles. As an example, we consider an elementary, singlephase, four-pole generator

shown in Figure 9. There are two complete cycles in the flux distribution around theperiphery as shown in Figure 10. The armature winding in this case consists of two coils ( a 1,


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-a 1, and a 2, -a 2) connected in series. The generated voltage goes through two completecycles per revolution of the rotor, and thus the frequency f in hertz is twice the speed inrevolutions per second. In general, the coil voltage of a machine with P-poles passes througha complete cycle every time a pair of poles sweeps by, or P/2 times for each revolution. Thefrequency f is therefore given by

( 1)where n is the shaft speed in revolutions per minute (r/min).

In treating P-pole synchronous machines, it is more convenient to express angles inelectrical degrees rather than in the more familiar mechanical units. Here we concentrate ona single pair of poles and recognize that the conditions associated with any other pair aresimply repetitions of those of the pair under consideration. A full cycle of generated voltagewill be described when the rotor of a four-pole machine has turned 180 mechanical degrees.

This cycle represents 360 electrical degrees in the voltage wave. Extending this argument toa P-pole machine leads to

( 2)

where e and m denote angles in electrical and mechanical degrees, respectively.

Figure 9: Four-Pole Synchronous Machine.

Figure 10: Space Distribution of Flux Density in a Four-Pole Synchronous Machine.


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The resultant magnetic field in the machine is the sum of the two contributions fromthe field and armature reaction. Figure 11 shows a sketch of the armature and field windingsof a cylindrical rotor generator. The space MMF produced by the field winding is shown bythe sinusoid F . This is shown for the specific instant when the electromotive force (EMF) ofphase a due to excitation has its maximum value. The time rate of change of flux linkageswith phase a is a maximum under these conditions, and thus the axis of the field is 90ahead of phase a . The armature-reaction wave is shown as the sinusoid A in the figure. Thisis drawn opposite phase a because at this instant both Ia and the EMF of the filed Ef (alsocalled excitation voltage) have their maximum value.

The resultant magnetic field in the machine is denoted R and is obtained bygraphically adding the F and A waves. Sinusoids can conveniently be handled using phasormethods. We can thus perform the addition of the A and F waves using phasor notation.Figure 12 shows a space phasor diagram where the fluxes f (due to the field), ar (due toarmature reaction), and r (the resultant flux) are represented. It is clear that under the

assumption of a uniform air gap and no saturation, these are proportional to the MMFwaves F , A, and R, respectively. The figure is drawn for the case when the armature currentis in phase with the excitation voltage.

Figure 11: Spatial MMF Waves in a Cylindrical Rotor Synchronous Generator.

Figure 12: A Space Phasor Diagram for Armature Current in Phase with Excitation Voltage.


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4.6 A S IMPLE E QUIVALENT C IRCUIT

The simplest model of a synchronous machine with cylindrical rotor can be obtainedif the effect of the armature-reaction flux is represented by an inductive reactance. The basisfor this is shown in Figure 13, where the phasor diagram of component fluxes and

corresponding voltages is given. The field flux f is added to the armature-reaction flux ar toyield the resultant air-gap flux r. The armature-reaction flux ar is in phase with thearmature current Ia. The excitation voltage E f is generated by the field flux, and E f lags f by90.

Similarly, E ar and E r are generated by ar and r respectively, with each of thevoltages lagging the flux causing it by 90.

Introduce the constant of proportionality x to relate the rms values of E ar and I a, towrite

( 9)

where the j represents the 90 lagging effect. We therefore have

( 10)

An equivalent circuit based on Eq. ( 10) is given in Figure 14. We thus conclude thatthe inductive reactance x accounts for the armature-reaction effects. This reactance isknown as the magnetizing reactance of the machine.

Figure 13: Phasor Diagram for Fluxes and Resulting Voltages in a Synchronous Machine

Figure 14: Two Equivalent Circuits for the Synchronous Machine.

The terminal voltage of the machine denoted by Vt is the difference between theair-gap voltage Er and the voltage drops in the armature resistance ra , and the leakage-reactance xl . Here xl accounts for the effects of leakage flux as well as space harmonic filedeffects not accounted for by x . A simple impedance commonly known as the synchronousimpedance Zs is obtained by combining x , xl , and ra according to

( 11)


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The synchronous reactance Xs is given by

( 12)The model obtained here applies to an unsaturated cylindrical rotor machine

supplying balanced polyphase currents to its load. The voltage relationship is now given by

( 13)

Example 1:

A 10 MVA, 13.8 kV, 60 Hz, two-pole, Y-connected, three-phase alternator has anarmature winding resistance of 0.07 ohms per phase and a leakage reactance of 1.9 ohmsper phase. The armature reaction EMF for the machine is related to the armature current by

Assume that the generated EMF is related to the field current by

A. Compute the field current required to establish rated voltage across theterminals of a load when rated armature current is delivered at 0.8 PF lagging.

B. Compute the field current needed to provide rated terminal voltage to a loadthat draws 100 per cent of rated current at 0.85 PF lagging.

Solution:

With reference to the equivalent circuit, we have


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4.7 P RINCIPAL S TEADY -S TATE C HARACTERISTICS

Consider a synchronous generator delivering power to a constant power factor loadat a constant frequency. A compounding curve shows the variation of the field currentrequired to maintain rated terminal voltage with the load. Typical compounding curves forvarious power factors are shown in Figure 15. The computation of points on the curvefollows easily from applying Eq. ( 13). Figure 16 shows phasor diagram representations forthree different power factors.

Figure 15: Synchronous-Machine Compounding Curves.

Example 2:

A 1,250-kVA, three-phase, Y-connected, 4,160-V (line-to-line), ten-pole, 60-Hzgenerator has an armature resistance of 0.126 ohms per phase and a synchronous reactanceof 3 ohms per phase. Find the full load generated voltage per phase at a power factor of 0.8lagging.

Solution:


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A characteristic of the synchronous machine is given by the reactivecapabilitycurves. These give the maximum reactive power loadings corresponding to various activepower loadings for rated voltage operation.

Armature heating constraints govern the machine for power factors from rated tounity. Field heating represents the constraints for lower power factors. Figure 17 shows atypical set of curves for a large turbine generator.

Figure 16: Phasor Diagrams for a Synchronous Machine Operating at Different Power Factors are: (a) Unity PFLoads, (b) Lagging PF Loads, and (c) Leading PF Loads.


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Figure 17: Generator Reactive-Capability Curves.

4.8 P OWER -A NGLE C HARACTERISTICS A ND T HE INFINITE B US

C ONCEPT

Consider the simple circuit shown in Figure 18. The impedance Z connects thesending end, whose voltage is E and receiving end, with voltage V . Let us assume that inpolar form we have

( 14)

( 15)

( 16)

We therefore conclude that the current I is given by

( 17)

The complex power S1 at the sending end is given by

( 18)

Similarly, the complex power S2 at the receiving end is

( 19)

Therefore,

( 20)


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( 21)

Recall that

( 22)

Figure 18: Equivalent Circuit and Phasor Diagram for a Simple Link.

When the resistance is negligible; then

( 23)and the power equations are obtained as:

( 24)

( 25)

( 26)

In large-scale power systems, a three-phase synchronous machine isconnected through an equivalent system reactance (Xe) to the network which has a highgeneration capacity relative to any single unit. We often refer to the network or system asan infinite bus when a change in input mechanical power or in field excitation to the unit

does not cause an appreciable change in system frequency or terminal voltage. Figure 19 shows such a situation, where V is the infinite bus voltage.

The previous analysis shows that in the present case we have for power transfer,

( 27)

With

( 28)And


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( 29)If we try to advance further than 90 (corresponding to maximum power transfer)

by increasing the mechanical power input, the electrical power output would decrease fromthe Pmax point. Therefore the angle increases further as the machine accelerates. Thisdrives the machine and system apart electrically. The value Pmax is called the steady-statestability limit or pull-out power.

Example 3:

A synchronous generator with a synchronous reactance of 1.15 p.u. is connected toan infinite bus whose voltage is one p.u. through an equivalent reactance of 0.15 p.u. Themaximum permissible output is 1.2 p.u.

A. Compute the excitation voltage E .

B. The power output is gradually reduced to 0.7 p.u. with fixed field excitation. Findthe new current and power angle .

Figure 19: A Synchronous Machine Connected to an Infinite Bus.

Solution:

A. The total resistance is

Thus we have,


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4.8.1 R EACTIVE P OWER G ENERATION

Eq. ( 26) suggests that the generator produces reactive power ( Q2 > 0) if

( 30)In this case, the generator appears to the network as a capacitor. This condition

applies for high magnitude E , and the machine is said to be overexcited. On the other hand,the machine is underexcited if it consumes reactive power ( Q2 < 0).

Here we have

( 31)

Figure 20 shows phasor diagrams for both cases. The overexcited synchronousmachine is normally employed to provide synchronous condenser action, where usually noreal load is carried by the machine ( = 0). In this case we have

( 32)

Control of reactive power generation is carried out by simply changing E , by varyingthe dc excitation.


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Figure 20: Phasor Diagrams for Overexcited and Underexcited Synchronous Machines.

Example 4:

Compute the reactive power generated by the machine of Example 3 under theconditions in part (b). If the machine is required to generate a reactive power of 0.4 p.u.while supplying the same active power by changing the filed excitation, find the newexcitation voltage and power angle .

Solution:

The reactive power generated is

With a new excitation voltage and stated active and reactive powers, we have


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Example 5:

A 5-k VA, 220-V, 60-Hz, six-pole, Y-connected synchronous generator has a leakagereactance per phase of 0.78 ohms and negligible armature resistance. The armature-reactionEMF for this machine is related to the armature current by

Assume that the generated EMF is related to field current by

A. Compute the field current required to establish rated voltage across the terminalsof a unity power factor load that draws rated generator armature current.

B. Determine the field current needed to provide rated terminal voltage to a loadthat draws 125 percent of rated current at 0.8 PF lagging.

Example 6:A 9375 kVA, 13,800 kV, 60 Hz, two pole, Y-connected synchronous generator is

delivering rated current at rated voltage and unity PF. Find the armature resistance andsynchronous reactance given that the filed excitation voltage is 11935.44 V and leads theterminal voltage by an angle 47.96.

Example 7:

The synchronous reactance of a cylindrical rotor machine is 1.2 p.u. The machine isconnected to an infinite bus whose voltage is 1 p.u. through an equivalent reactance of 0.3p.u. For a power output of 0.7 p.u., the power angle is found to be 30.

A. Find the excitation voltage Ef and the pull-out power.

B. For the same power output the power angle is to be reduced to 25. Find thevalue of the reduced equivalent reactance connecting the machine to the bus to achievethis. What would be the new pullout power?

Example 8:

The synchronous reactance of a cylindrical rotor machine is 0.8 p.u. The machine isconnected to an infinite bus through two parallel identical transmission links with reactanceof 0.4 p.u. each. The excitation voltage is 1.4 p.u. and the machine is supplying a load of 0.8p.u.

A. Compute the power angle for the outlined conditions.

B. If one link is opened with the excitation voltage maintained at 1.4 p.u. Find thenew power angle to supply the same load as in (a).

Example 9:

The synchronous reactance of a cylindrical rotor machine is 0.9 p.u. The machine isconnected to an infinite bus through two parallel identical transmission links with reactanceof 0.6 p.u. each. The excitation voltage is 1.5 p.u., and the machine is supplying a load of 0.8p.u.


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A. Compute the power angle for the given conditions.

B. If one link is opened with the excitation voltage maintained at 1.5 p.u., find thenew power angle to supply the same load as in part (a).

Example 10:

Solution:


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Example 11:

The generator of Example 10 is delivering 40 MW at a terminal voltage of 30 kV.Compute the power angle, armature current, and power factor when the field current isadjusted for the following excitations.

(a) The excitation voltage is decreased to 79.2 percent of the value found inExample 10.

(b) The excitation voltage is decreased to 59.27 percent of the value found inExample 10.

(c) Find the minimum excitation below which the generator will lose synchronism.

Solution:


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Intorduction to Power Engineering - 4 Generators