Chapter Five Synchronous Generators

Transcription

1 Chapter Five Synchrnus Generatrs 5.1 Intrductin Three phase synchrnus generatrs are the primary surce f all the electrical energy we cnsume. These machines are the largest energy cnverters in the wrld. They cnvert mechanical energy int electrical energy, in pwers ranging up t 1500 MW. In this chapter we will study the cnstructin and characteristics f these large, mdern generatrs. They are based upn the elementary principles. 5.2 Cmmercial Synchrnus Generatrs Cmmercial synchrnus generatrs are built with either a statinary r a rtating DC magnetic field. A statinary field synchrnus generatr has the same utward appearance as a DC generatr. The salient ples create the DC field, which is cut by a revlving armature. The armature pssesses a 3-phase winding whse terminals are cnnected t three slip-rings munted n the shaft. A set f brushes, sliding n the slip-rings, enables the armature t be cnnected t an external 3-phase lad. The armature is driven by a gasline engine, r sme ther surce f mtive pwer. As it rtates, a 3-phase vltage is

2 .254 Chapter Five induced, whse value depends upn the speed f rtatin and upn the DC exciting current in the statinary ples. The frequency f the vltage depends upn the speed and the number f ples n the field. Statinary-field generatrs are used when the pwer utput is less than 5 kva. Hwever, fr greater utputs, it is cheaper, safer, and mre practical t emply a revlving DC field. A revlving field synchrnus generatr has a statinary armature called a statr. The 3-phase statr winding is directly cnnected t the lad, withut ging thrugh large, unreliable slip-rings and brushes. A statinary statr als makes it easier t insulate the windings because they are nt subjected t centrifugal frces. Fig.5.1 is a schematic diagram f such a generatr, smetimes called an alternatr. The field is excited by a DC generatr, usually munted n the same shaft. Nte that the brushes n the cmmutatr have t be cnnected t anther set f brushes riding n slip-rings t feed the DC current I X int the revlving field. Fig.5.1Schematic diagram and crss-sectin view f a typical 500 MW synchrnus generatr.

3 Synchrnus Generatrs Number f Ples The number f ples n a synchrnus generatr depends upn the speed f rtatin and the frequency we wish t prduce. Cnsider, fr example, a statr cnductr that is successively swept by the N and S ples f the rtr. If a psitive vltage is induced when an N ple sweeps acrss the cnductr, a similar negative vltage is induced when the S ple speeds by. Thus, every time a cmplete pair f ples crsses the cnductr, the induced vltage ges thrugh a cmplete cycle. The same is true fr every ther cnductr n the statr; we can therefre deduce that the alternatr frequency is given by Pn f = (5.1) 120 f =frequency f the induced vltage [Hz]. P = number f ples n the rtr. n = speed f the rtr [r/min]. Example 5.1 A hydraulic turbine turning at 200 r/min is cnnected t a synchrnus generatr. If the induced vltage has a frequency f 60 Hz, hw many ples des the rtr have? Slutin: Frm Eqn.(5.1), we have : P= 120 * 60/200 = 36 ples, r 18 pairs f N and S ples.

4 .256 Chapter Five 5.4 Main Features Of The Statr Frm an electrical standpint, the statr f a synchrnus generatr is identical t that f a 3-phase inductin mtr. It is cmpsed f a cylindrical laminated cre cntaining a set f slts that carry a 3-phase lap winding. The winding is always cnnected in wye and the neutral is cnnected t grund. A wye cnnectin is preferred t a delta cnnectin because: 1. The vltage per phase is nly 1 / 3 r 58% f the vltage between the lines. This means that the highest vltage between a statr cnductr and the grunded statr cre is nly 58% f the line vltage. We can therefre reduce the amunt f insulatin in the slts that in turn, enables us t increase the crss sectin f the cnductrs. A larger cnductr permits us t increase the current and, hence, the pwer utput f the machine. 2. When a synchrnus generatr is under lad, the vltage induced in each phase becmes distrted, and the wavefrm is n lnger sinusidal. The distrtin is mainly due t an undesired third harmnic vltage whse frequency is three times that f the fundamental frequency. With a wye cnnectin, the distrting line-t-neutral harmnics d nt appear between the lines because they effectively cancel each ther. Cnsequently, the line vltages remain sinusidal under all lad cnditins. Unfrtunately, when a delta cnnectin is used, the harmnic vltages d nt cancel, but

5 Synchrnus Generatrs 257 add up. Because the delta is clsed n itself, they prduce a third-harmnic circulating current, which increases the I 2 R lsses. The nminal line vltage f a synchrnus generatr depends upn its kva rating. In general, the greater the pwer rating, the higher the vltage. Hwever, the nminal line-t-line vltage seldm exceeds 25 kv because the increased slt insulatin takes up valuable space at the expense f the cpper cnductrs. 5.5 Main Features Of The Rtr Synchrnus generatrs are built with tw types f rtrs: salient ple rtrs and smth, cylindrical rtrs. Salient ple rtrs are usually driven by lw-speed hydraulic turbines, and cylindrical rtrs are driven by high-speed steam turbines. 1. Salient ple rtrs. Mst hydraulic turbines have t turn at lw speeds (between 50 and 300 r/min) in rder t extract the maximum pwer frm a waterfall. Because the rtr is directly cupled t the waterwheel, and because a frequency f 50 Hz r 60 Hz is required, a large number f ples are required n the rtr. Lw-speed rtrs always pssess a large diameter t prvide the necessary space fr the ples. The salient ples are munted n a large circular steel frame which is fixed t a revlving vertical shaft. T ensure gd cling, the field cils are made f bare cpper bars, with the turns insulated frm each ther by strips f

6 .258 Chapter Five mica. The cils are cnnected in series, with adjacent ples having ppsite plarities. In additin t the DC field winding, we ften add a squirrel-cage winding, embedded in the ple faces. Under nrmal cnditins, this winding des nt carry any current because the rtr turns at synchrnus speed. Hwever, when the lad n the generatr changes suddenly, the rtr speed begins t fluctuate, prducing mmentary speed variatins abve and belw synchrnus speed. This induces a vltage in the squirrel-cage winding, causing a large current t flw therein. The current reacts with the magnetic field f the statr, prducing frces which dampen the scillatin f the rtr. Fr this reasn, the squirrel-cage winding is smetimes called a damper winding. The damper winding als tends t maintain balanced 3-phase vltages between the lines, even when the line currents are unequal due t unbalanced lad cnditins. 2. Cylindrical rtrs. It is well knwn that high-speed steam turbines are smaller and mre efficient than lw-speed turbines. The same is true f high-speed synchrnus generatrs. Hwever, t generate the required frequency we cannt use less than 2 ples, and this fixes the highest pssible speed. On a 60 Hz system it is 3600 r/min. The next lwer speed is 1800 r/min, crrespnding t a 4-ple machine. Cnsequently, these steam-turbine generatrs pssess either 2 r 4 ples.

7 Synchrnus Generatrs 259 The rtr f a turbine-generatr is a lng, slid steel cylinder which cntains a series f lngitudinal slts milled ut f the cylindrical mass. Cncentric field cils, firmly wedged int the slts and retained by high-strength end-rings serve t create the N and S ples. The high speed f rtatin prduces strng centrifugal frces, which impse an upper limit n the diameter f the rtr. In the case f a rtr turning at 3600 r/min, the elastic limit f the steel requires the manufacturer t limit the diameter t a maximum f 1.2 m. On the ther hand, t build the pwerful 1000 MVA t 1500 MVA generatrs the vlume f the rtrs has t be large. It fllws that high-pwer, high-speed rtrs have t be very lng. 5.6 Field Excitatin And Exciters The DC field excitatin f a large synchrnus generatr is an imprtant part f its verall design. The reasn is that the field must ensure nt nly a stable ac terminal vltage, but must als respnd t sudden lad changes in rder t maintain system stability. Quickness f respnse is ne f the imprtant features f the field excitatin. In rder t attain it, tw DC generatrs are used: a main exciter and a pilt exciter Static exciters that invlve n rtating parts at all are als emplyed. The main exciter feeds the exciting current t the field f the synchrnus generatr by way f brushes and slip-rings. Under

8 .260 Chapter Five nrmal cnditins the exciter vltage lies between 125 V and 600 V. It is regulated manually r autmatically by cntrl signals that vary the current I c, prduced by the pilt exciter (Fig.5.1). The pwer rating f the main exciter depends upn the capacity f the synchrnus generatr. Typically, a 25 kw exciter is needed t excite a 1000 kva alternatr (2.5% f its rating) whereas a 2500 kw exciter suffices fr an alternatr f 500 MW (nly 0.5% f its rating). Under nrmal cnditins the excitatin is varied autmatically. It respnds t the lad changes s as t maintain a cnstant ac line vltage r t cntrl the reactive pwer delivered t the electric utility system. A serius disturbance n the system may prduce a sudden vltage drp acrss the terminals f the alternatr. The exciter must then react very quickly t keep the ac vltage cnstant. Fr example, the exciter vltage may have t rise t twice its nrmal value in as little as 300 t 400 millisecnds. This represents a very quick respnse, cnsidering that the pwer f the exciter may be several thusand kilwatts. 5.7 Brushless Excitatin Due t brush wear and carbn dust, we cnstantly have t clean, repair, and replace brushes, slip-rings, and cmmutatrs n cnventinal DC excitatin systems. T eliminate the prblem, brushless excitatin systems have been develped. Such a system

9 Synchrnus Generatrs 261 cnsists f a 3-phase statinary field generatr whse ac utput is rectified by a grup f rectifiers. The DC utput frm the rectifiers is fed directly int the field f the synchrnus generatr (Fig.5.2). Fig.5.2 Brushless exciter system. The armature f the ac exciter and the rectifiers are munted n the main shaft and turn tgether with the synchrnus generatr. In cmparing the excitatin system f Fig.5.2 with that f Fig.5.1, we can see they are identical, except that the 3-phase rectifier replaces the cmmutatr, slip rings, and brushes. In ther wrds, the cmmutatr (which is really a mechanical rectifier) is replaced by an electrnic rectifier. The result is that the brushes and slip-rings are n lnger needed. The DC cntrl current I c frm the pilt exciter regulates the main exciter utput I x, as in the case f a cnventinal DC exciter. The frequency f the main exciter is generally tw t three times

10 .262 Chapter Five the synchrnus generatr frequency (50 Hz). The increase in frequency is btained by using mre ples n the exciter than n the synchrnus generatr. Static exciters that invlve n rtating parts at all are als emplyed. 5.8 Factrs Affecting The Size Of Synchrnus Generatrs The prdigius amunt f energy generated by electrical utility cmpanies has made them very cnscius abut the efficiency f their generatrs. Fr example, if the efficiency f a 1000 MW generating statin imprves by nly 1 %, it represents extra revenues f several thusand dllars per day. In this regard, the size f the generatr is particularly imprtant because its efficiency autmatically imprves as the pwer increases. Fr example, if a small 1 kilwatt synchrnus generatr has an efficiency f 50%, a larger, but similar mdel having a capacity f 10 MW inevitably has an efficiency f abut 90%. This imprvement in efficiency with size is the reasn why synchrnus generatrs f 1000 MW and up pssess efficiencies f the rder f 99%. Anther advantage f large machines is that the pwer utput per kilgram increases as the pwer increases. Fr example, if a 1 kw generatr weighs 20 kg (yielding 1000 W/20 kg = 50 W/kg), a 10 MW generatr f similar cnstructin will weigh nly

11 Synchrnus Generatrs 263 kg, thus yielding 500 W/kg. Frm a pwer standpint, large machines weigh relatively less than small machines; cnsequently, they are cheaper. Sectin at the end f this chapter explains why the efficiency and utput per kilgram increase with size. Everything, therefre, favrs the large machines. Hwever, as they increase in size, we run int serius cling prblems. In effect, large machines inherently prduce high pwer lsses per unit surface area (W/m 2 ); cnsequently, they tend t verheat. T prevent an unacceptable temperature rise, we must design efficient cling systems that becme ever mre elabrate as the pwer increases. Fr example, a circulating cld air system is adequate t cl synchrnus generatrs whse rating is belw 50 MW but between 50 MW and 300 MW we have t resrt t hydrgen cling. Very big generatrs in the 1000 MW range have t be equipped with hllw, water-cled cnductrs. Ultimately, a pint is reached where the increased cst f cling exceeds the savings made elsewhere, and this fixes the upper limit t size. T sum up, the evlutin f big alternatrs has mainly been determined by the evlutin f sphisticated cling techniques. Other technlgical breakthrughs, such as better materials, and nvel windings have als played a majr part in mdifying the design f early machines. As regards speed, lw-speed generatrs are always bigger than high-speed machines f equal pwer. Slw-speed bigness

12 .264 Chapter Five simplifies the cling prblem; a gd air-cling system, cmpleted with a heat exchanger, usually suffices. Fr example, the large, slw-speed 500 MVA, 200 r/min synchrnus generatrs installed in a typical hydrpwer plant are air-cled whereas the much smaller high-speed 500 MVA, 1800 r/min units installed in a steam plant have t be hydrgen-cled. 5.9 N-Lad Saturatin Curve Fig.5.3 shws a 2-ple synchrnus generatr perating at n-lad. It is driven at cnstant speed by a turbine. The leads frm the 3-phase, wye-cnnected statr are brught ut t terminals A, B, C, N, and a variable exciting current I X prduces the flux in the air gap. Fig.5.3 Generatr peratin at n-lad.

13 Synchrnus Generatrs 265 Let us gradually increase the exciting current while bserving the ac vltage E between terminal A, say, and the neutral N. Fr small values f I X, the vltage increases in direct prprtin t the exciting current. Hwever, as the irn begins t saturate, the vltage rises much less fr the same increase in I X. If we plt the curve f E versus I X, we btain the n-lad saturatin curve f the synchrnus generatr. Fig.5.4 shws the actual n-lad saturatin curve f a 36 MW, 3-phase generatr having a nminal vltage f 12 kv (line t neutral). Up t abut 9 kv, the vltage increases in prprtin t the current, but then the irn begins t saturate. Thus, an exciting current f 100 A prduces an utput f 12 kv, but if the current is dubled, the vltage rises nly t 15 kv.

14 .266 Chapter Five Fig.5.5 is a schematic diagram f the generatr shwing the revlving rtr and the three phases n the statr. Fig.5.5 Electric circuit representing the generatr f Fig.5.3

15 Synchrnus Generatrs Synchrnus Reactance Equivalent Circuit Of An Ac Generatr Cnsider a 3phase synchrnus generatr having terminals A, B, C feeding a balanced 3phase lad. The generatr is driven by a turbine, and is excited by a DC current I X. The machine and its lad are bth cnnected in wye, yielding the circuit f Fig.5.6. Althugh neutrals N 1 and N 2 are nt cnnected, they are at the same ptential because the lad is balanced. Cnsequently, we culd cnnect them tgether (as indicated by the shrt dash line) withut affecting the behavir f the vltages r currents in the circuit. The field carries an exciting current which prduces a fluxφ. As the field revlves, the flux induces in the statr three equal vltages E that are 120 degrees ut f phase (Fig.5.7). Each phase f the statr winding pssesses a resistance R and a certain inductance L. Because this Fig.5.6 Electric circuit representing the alternatr cnnected with 3-phase lad.

16 .268 Chapter Five Fig.5.7 Vltage and impedances in a 3-phase generatr and its cnnected lad The synchrnus reactance f a generatr is an internal impedance, just like its internal resistance R. The impedance is there, but it can neither be seen nr tuched. The value f X S is typically 10 t 100 times greater than R; cnsequently, we can always neglect the resistance, unless we are interested in efficiency r heating effects. We can simplify the schematic diagram f Fig.5.7 by shwing nly ne phase f the statr. In effect, the tw ther phases are identical, except that their respective vltages (and currents) are ut f phase by 120 degrees. Furthermre, if we neglect the resistance f the windings, we btain the very simple circuit f Fig.5.8. A synchrnus generatr can therefre be represented by an equivalent circuit cmpsed f an induced vltage E in series with a reactance X S.

17 Synchrnus Generatrs 269 Fig.5.8 Equivalent circuit f a 3-phase generatr, shwing nly ne phase. In this circuit the exciting current I X prduces the flux φ which induces the internal vltage E. Fr a given synchrnus reactance, the vltage E at the terminals f the generatr depends upn E and the lad Z. Nte that vltages and I is the line current. E and E are line-t-neutral Example 5.2 A 3-phase synchrnus generatr prduces an pen-circuit line vltage f 6928 V when the d exciting current is 50 A. The ac terminals are then shrt-circuited, and the three line currents are fund t be 800 A. a. Calculate the synchrnus reactance per phase. b. Calculate the terminal vltage if three 12 Ω resistrs are cnnected in wye acrss the terminals. Slutin: a. The line-t-neutral induced vltage is E = EL / 3 = 6928/ 3 = 4000V

18 .270 Chapter Five When the terminals are shrt-circuited, the nly impedance limiting the current flw is that due t the synchrnus reactance. Cnsequently, X S = E / I = 4000 / 80 = 5Ω The synchrnus reactance per phase is therefre 5 fl. b. The equivalent circuit per phase is shwn in Fig.5.9a. The impedance f the circuit is: Z = R + = = 13Ω X S The current is : I = E / Z = 4000 /13 = 308A The vltage acrss the lad resistr is E = IR = 308 *12 = 3696 V The line vltage under lad is: E L = 3 E = 3 *3696 = 6402 V The schematic diagram f Fig.5.9b helps us visualize what is happening in the actual circuit.

19 Synchrnus Generatrs 271 Fig.5.9. See Example 5.2. b. Actual line vltages and currents Synchrnus Generatr Under Lad The behavir f a synchrnus generatr depends upn the type f lad it has t supply. There are many types f lads, but they can all be reduced t tw basic categries: 1. -Islated lads, supplied by a single generatr 2.-Cnsider a 3-phase generatr that supplies pwer t a lad having a lagging pwer factr. Fig.5.10 represents the equivalent circuit fr ne phase. In rder t cnstruct the phasr diagram fr this circuit, we list the fllwing facts: Fig.5.10 Equivalent circuit f a generatr under lad.

20 .272 Chapter Five 1. Current I lags behind terminal vltage E by an angle θ. 2. Csine θ = pwer factr f the lad. 3. Vltage E X acrss the synchrnus reactance leads current I by E = jix. 90 degrees. It is given by the expressin x S 4. Vltage E generated by the flux φ is equal t the phasr sum f E plus E X. 5. Bth E and E X are vltages that exist inside the synchrnus generatr windings and cannt be measured. 6. Flux φ is that prduced by the DC exciting current I x. The resulting phasr diagram is given in Fig Nte that leads E by δ degrees. Furthermre, the internally-generated vltage E is greater than the terminal vltage, as we wuld expect. E In sme cases the lad is smewhat capacitive, s that current I leads the terminal vltage by an angle θ. What effect des this have n the phasr diagram? The answer is fund in Fig The vltage E X acrss the synchrnus reactance is still 90 degrees ahead f the current. Furthermre, E O is again equal t the phasr sum f E and E X. Hwever, the terminal vltage is nw greater than the induced vltage E O, which is a very surprising result. In

21 Synchrnus Generatrs 273 effect, the inductive reactance X S enters int partial resnance with the capacitive reactance f the lad. Althugh it may appear we are getting smething fr nthing, the higher terminal vltage des nt yield any mre pwer. If the lad is entirely capacitive, a very high terminal vltage can be prduced with a small exciting current. Hwever, in later chapters, we will see that such under-excitatin is undesirable. Fig.5.11 Phasr diagram fr a lagging pwer factr lad. Fig5.12 Phasr diagram fr a leading pwer factr lad. Example 5.3 A 36 MVA, 20.8 kv, 3-phase alternatr has a synchrnus reactance f 9Ω and a nminal current f 1 ka. The n-lad saturatin curve giving the relatinship between E and I, is given in Fig.5.5. If the excitatin is adjusted s that the terminal

22 .274 Chapter Five vltage remains fixed at 21 kv, calculate the exciting current required and draw the phasr diagram fr the fllwing cnditins: a. N-lad b. Resistive lad f 36 MW c. Capacitive lad f 12 Mvar Slutin: We shall immediately simplify the circuit t shw nly ne phase. The line-t-neutral terminal vltage fr all cases is fixed at E = 20.8/ 3 = 12 kv a. At n-lad there is n vltage drp in the synchrnus reactance; cnsequently, E = E = 12 kv The exciting current is : I x = 100 A (See Fig.5.5) In n lad E and E will be in phase With a resistive lad f 36 MW: b. The pwer per phase is P=36/3=12 MW The full lad line current is 6 I = P / E = 12*10 / = 1000 A

23 Synchrnus Generatrs 275 The current is in phase with the terminal vltage. The vltage acrss X S is: E = jx = j1000*9 = 9 kv 90 x S The vltage E generated by Ix is equal t the phasr sum f E and E x Referring t the phasr diagram, its value is given by: E = E + Ex = = 15 The required exciting current is I x = 200 A (See Fig.5.5) kv The phasr diagram is given in Fig Fig.5.13 Phasr diagram with a unity pwer factr lad. With a capacitive lad f 12 Mvar: c. The reactive pwer per phase is Q=12/3=4 Mvar. The line current is 6 I = Q / E = 4*10 /12000 = 333A

24 .276 Chapter Five The vltage acrss X S is Ex = jx S = j333*9 = 3 90 As befre kv E x leads I by 90 degrees. (Fig.5.14) Fig.5.14 Phasr diagram with a capacitive lad. The vltage E generated by I x is equal t the phasr sum f E x and E. ( 3) kv E = E + Ex = 12 + = 9 The crrespnding exciting current is I x = 70 A (See Fig.5.5) Nte that E is again less than the terminal vltage E. The phasr diagram fr this capacitive lad is given in Fig.5.14.