Electrical Motors/Generator Technology

Transcription

1 John Driesen, Ronnie Belmns K.U.Leuven, Deprtment Electricl Engineering (ESAT) Div. ESAT/ELECTA Ksteelprk Arenberg 0 B-300 Leuven BELGUM NTRODUCTON Devices, trnsforming energy by electromgnetic processes re understood s electricl mchines. There re three types of devices for energy conversion tht cn be distinguished: Trnsformers re converters trnsforming electricl energy into nother form of electricl energy with different properties (voltge, current); Motors where the electricl energy is converted into mechnicl energy; nd Genertors for generting electricl energy from mechnicl energy. Motors nd genertors re in fct the sme devices s electromgnetic-electromechnicl energy conversion is reversible. So when motor brkes, it will reverse the power consumption nd try to put power bck into the supply. The vst mjority of electricl mchines uses mgnetic force principles to chieve the conversion. Electricl forces, bsed upon the ttrction of chrges, re in generl too wek for prcticl pplictions nd re only used in (silicon) micromchines or microphones. Mgnetic forces rise due to the minimiztion of mgnetic field energy. For instnce, when permnent mgnet is close to piece of ferromgnetic iron, it is ttrcted s the field energy is minimized when the ir gp between the two pieces is s smll s possible. n fct this sort of force, clled reluctnce force, is induced in movble or deformble structures by single mgnetic field until minimum of field energy is ttined. This force cuses ll sorts of ttrction nd lignment, for instnce in mchines with (mgnetic) symmetricl shpes. Reluctnce is to be understood s mgnetic equivlent to resistnce (to mgnetic flux insted of electricl current). Driesen, J.; Belmns, R. (005) Electricl Motors/Genertor Technology. n Micro Gs Turbines (pp. - -8). Eductionl Notes RTO-EN-AVT-3, Pper. Neuilly-sur-Seine, Frnce: RTO. Avilble from: RTO-EN-AVT-3 -

2 Figure.: The Reluctnce Torque (4) Aligns the Rotor (). However, the best known mgnetic force is the force on current crrying conductor in mgnetic field, the Lorentz force: the force is proportionl to the mgnetic induction of the field, the current in the wire nd the length of the wire: F = B l (.) This is in fct equivlent to field-energy minimiztion ppliction s the current in the wire cuses concentric mgnetic field round it nd the totl mgnetic field is minimized by pushing this out. Such field minimiztion by interction of two (independent) mgnetic fields, cusing powerful forces nd torques, is used in most electricl mchines, s it is in generl more powerful thn the reluctnce force, but the current involved cuses Joule losses. Figure.: Lorentz Force Principle: () superimposed mgnetic field, (b-c) force minimizing field energy. n the following sections the bsic concepts nd principles of the most importnt electricl motors/ genertors re introduced. Their function nd fundmentl opertionl behviour will be discussed..0 DC MACHNE The DC mchine cn operte s either genertor or motor. ts use s genertor is limited to smll units, e.g. the bicycle lighting dynmo, nd specil genertor pplictions. The DC motors cn still be found in vrious pplictions, such s mchine tools (drills), printing presses, fns, pumps, crnes, textile mills, etc. However, it must be noted tht due to severl resons: decresing costs for power electronic control circuits nd the less expensive purchse nd mintennce cost of induction mchines, the DC mchine is more nd more vnishing from the mrket. Approximtely 95% of ll current electricl motors re - RTO-EN-AVT-3

3 vrible-speed induction motors. Nevertheless, it is included s it forms the most bsic electromgnetic ctutor from which most other drives re inherited. DC motors re nowdys still pplied in vrible-speed drives, with power electronic supply. Advntgeous is the simple construction nd structure of the sttic converter, the high control-dynmic nd its high power-density. Disdvntgeous is the required mintennce of the brushes nd the collector, which lso limit its mximum speed to few krpm. The fundmentl opertionl behviour of DC mchine cn be understood very quickly by pplying the induction lw on conductor moving in sttic mgnetic field: U i = NdΦ / dt (.) The induced voltge U i is proportionl to the time-vrying flux enclosed by the circuit. n the cse illustrted in Fig.., the flux vrition is obtined by the vrition of the coil-surfce A penetrted by the flux. N is the number of windings. U = NB da/ dt = NB ds / dt NB l v (.) i = δ δ δ fe B δ l fe U i U i ds v = ds / dt Figure.: Moving Coil in Mgnetic Field B δ. Due to the flux vrition voltge is induced in the coil tht is proportionl to: flux density B velocity of the conductor(s) v This principle cn directly be used to develop -pole rotting DC mchine. Motor s well s genertor opertion cn be derived from Fig... The collector or commuttor gurntees the unidirectionlity of the current. i 3 A b B N i S i 4 sttor pole winding 3 collector 4 direction of rottion A N b S B N B b S A Figure.: Principle of Rotting DC Mchine. RTO-EN-AVT-3-3

4 f it is ssumed tht the coil-surfce re A covers n entire pole pitch τ it cn be written: With the rotor rdius R nd p poles in the mchine, the pole pitch τ is: the pole-flux cn be clculted by: A = ατl fe (.3) πr τ =, (.4) p Φ = AB = ατl B δ fe δ (.5) The multipliction of in the mgnetic ir gp field B δ moving conductors z per winding brnch yields using eq. (.) the induced voltge in the rmture winding: z z U = α B l v = α B l πrn (.6) i δ fe δ fe n is the speed of the rotor, the number of prllel brnches. All quntities re given in the bsic unit system. With eq. (.5) the induced voltge is finlly clculted by the following expression, clerly showing the proportionlity of the induced voltge or electromgnetic force (emf) to the flux nd speed: U i z = pφn = k Φn (.7) Fig..3 illustrtes the term of the number of prllel winding-brnches. The winding current is lwys =. q-xis / / S D N d-xis U i U i Figure.3: DC Mchine with p= Poles nd = Prllel Winding Brnches. Supplying the DC mchine with voltge U t the terminls of the rotor, lso clled the rmture i.e. t the brushes (Fig..4), ssuming constnt voltge U f for the excittion winding nd neglecting the brushvoltge drop, the Kirchoff voltge lw yields: U = R + U (.8) i - 4 RTO-EN-AVT-3

5 + + ω r U i U f - U f - Figure.4: Voltge Systems for the DC Mchine. By multiplying with the rmture current trnsforms the voltge eqution (.8) into power blnce. U el = R + U P = P loss + P mech i (.9) t must be noted tht eq. (.9) only considers the Joule losses in the rmture winding nd neglects iron losses, friction nd the Joule losses in the excittion winding. The excittion winding s Joule losses hve to be considered determining the efficiency of the mchine. With the rrow system indicting the reltion between voltges nd currents in Fig..5, the different terms for the power cn be either in motor or genertor opertion dependent of the sign of the rmture current. For positive currents the mchine opertes s motor, respectively s genertor, if the rmture current is negtive. P loss U R L U i P el U f, f P mech Figure.5: Equivlent Circuit for DC Mchine. The reltion between the power nd speed of rotting system the DC mchine (.). P mech = U i = k Φ n = T πn P mech = Tω = T πn delivers the torque of (.0) ron losses re losses in ferromgnetic mteril due to chnging mgnetic flux. They consist of hysteresis losses (rising when the mterils BH hystereris loop is circulted) nd internl eddy current (induced currents) losses. RTO-EN-AVT-3-5

6 T k π = Φ = k Φ (.) Note tht the expression for the torque cn lso be derived by strting from the Lorentz force expression. Arrnging eq. (.8) nd (.) yields the importnt eqution for the reltion between speed nd torque: U R R n = T = n T. (.) k 0 Φ k k Φ k k Φ The no-lod speed of the DC mchine is n 0. This expression illustrtes tht the speed of the mchine decreses when loded, n effect tht hs to be corrected through feedbck control loop. Using eq. (.) enbles the prediction of the behviour of the DC mchine operted under vrious conditions nd different winding rrngements. Fig..6 shows the cross-section of DC motor to illustrte the flux pth in this mchine. t is obvious tht due to the commuttion of the rotor current, iron losses occur in the rotor nd DC mgnetic flux is situted in the sttor prt of the mchine. 3 min flux stry flux 3 field winding Z N 4 rotor 4 Figure.6: Bsic Construction of 4-Pole DC Mchine With nd Without nterpolr-gp Winding. Using the eqution (.9), (.) nd (.) the behviour nd the vrious possible opertions of DC mchine cn be studied. The possibilities to control the speed of this type of mchine cn be derived from such equtions s well. ndependently excited mchine: Applying seprte voltge source to the field winding or using permnent mgnet mteril for the sttor excittion yields the bsic chrcteristic of the DC mchine (Fig..7). t cn be seen tht this opertion with constnt flux cn be determined by evluting eqs. (.) nd (.). The continuously chnge to genertor opertion is possible t this opertion. + T, ω r T + ω r ω r E r U b - - U b GENERATOR MOTOR Figure.7: Seprtely Excited DC Mchine nd its Opertionl Chrcteristic. - 6 RTO-EN-AVT-3

7 Shunt or prllel excittion: Under this opertion, the excittion winding is rrnged in prllel to the rmture winding (Fig..8). + b + ω r b T, ω r b T ω r U E r GENERATOR MOTOR Figure.8: Shunt or Prllel Excittion. Series excittion: DC Trction drives require lrge torque t low speed nd low torque t high speeds. This desired chrcteristic cn be obtined by rrnging the excittion winding in series with the rmture winding (Fig..9). A continuous trnsition to the genertor opertion is not possible in this mode of opertion. Such mchine cn lso be supplied by AC current, s it cn be shown tht the torque is proportionl to the squre of the current. Therefore, it is better known s the universl motor, which smll chep single-phse mchine. This AC type of motor cn be found in the power rnge up to kw operting household pplictions, such s vcuum clener, drilling mchines etc. They re usully constructed s -pole motors. ts high power density is reched by operting t high speeds of bout to rpm. T, ω r T + + ω r ω r U E r - - ω r GENERATOR MOTOR Figure.9: Series Excittion of DC Motor. 3.0 NDUCTON MACHNE The induction mchine, lso know s synchronous mchine, is the most widely used electricl motor in industry. The reson for this cn be found in its very cost effective nd robust construction. nduction mchines re minly employed s motors up to 0 MW. Typicl res of ppliction re pump drives, vns, compressors, pper mills, etc. Sometimes induction mchines re used s genertors up to few MW, for instnce in certin types of wind turbines. nduction motors re operted by symmetric three-phse AC current/voltge system. Usully the induction motor consists of three-phse sttor winding, though smller (cheper) types cn be constructed with RTO-EN-AVT-3-7

8 single-phse AC windings. n the following section symmetricl three-phse mchines for industril pplictions re ssumed. nduction mchines hve uniform ir gp nd re operted by synchronously rotting mgnetic ir gp field excited by the sttor winding. The rotor is rotting synchronously (due to induction effects: see next prgrphs) with slip or reltive speed difference: n n s = (3.) n With the slip definition, the vrious opertion conditions of n induction mchine re given by: n < 0 s > 0 rottion ginst the rottionl field (brking) n = 0 s = locked rotor (stndstill) 0 < n < n > s > 0 opertion below synchronism (motor) n = n s = 0 Synchronism (idel no-lod) n > n s < 0 opertion bove synchronism (genertor) Bsiclly two rotor vrints of the induction motor (Fig. 3.) cn be distinguished: Squirrel cge (Fig. 3.): cst luminium (or sometimes copper) brs, short-circuited by ring-shped conductors t the end. Three-phse slip-ring rotor winding, the wound rotor type (Fig. 3.3): three-phse winding is present on the rotor s well. The windings re connected to slip-rings. This type ws used in the pst to chnge speeds by connecting extr resistnce externlly, but nowdys it is minly pplied in lrge doubly-fed mchine, where reltively smll power electronic supply is connected to the rotor in order to chieve vrible speed. A typicl exmple re lrge vrible-speed wind turbine genertor, connected to fixed-frequency power grid Figure 3.: Construction of n nduction Motor. ( ventiltor, ventiltor cp, 3 three-phse sttor winding, 4 sttor lmintion, 5 rotor cge (rotor brs nd end-ring), 6 rotor lmintion, 7 terminls, 8 grounding, 9 suspension, 0 suspension cp, continer for suspension oil, shft, 3 cool fins, 4 housing). - 8 RTO-EN-AVT-3

9 end-ring rotor br rotor lmintion slip-ring brushes end-winding rotor brs strt-up resistors three-phse winding Figure 3.: Rotor Winding Vrints: Squirrel Cge. Figure 3.3: Rotor Winding Vrints: Wound Rotor. The sttor is operted with the supply frequency f nd the rotor winding contins current nd voltges with slip-frequent AC currents with frequency: s.f. Therefore, the rotor nd sttor re constructed with iron lmintion, to prevent excessive eddy current losses in the mssive conducting structures. The sttor coils re rrnged in the slots of the sttor (Fig. 3.4). Low-voltge windings hve coils in hlf closed slots nd high-voltge mchines re constructed hving pre-mnufctured windings (Fig. 3.4). Concentric coils nd coils with the sme width cn be constructed. concentric coil w coils with sme width w l w w Figure 3.4: Winding Arrngements nd Slot Constructions for Low- nd High-Voltge Mchines. RTO-EN-AVT-3-9

10 The three-phse sttor winding is supplied by symmetric three-phse AC voltge or current system. The mgnitude of the winding currents must be identicl in ll identicl winding phses nd is shifted in time by 0 (electricl) degrees. The winding phses re displced from ech other by 0 (electricl) degrees in spce round the inner circumference of the mchine (Fig. 3.4). Under this ssumption rotting mgnetic field is generted in the ir gp of the mchine. This rotting mgnetic field is sensed by the rotor windings, seeing chnging mgnetic field nd hence voltge is induced. n the closed windings current will flow due to Ohm s lw nd this current s interction with the rotting mgnetic field cuses the torque. f the rotor would spin t the sme speed s the rotting mgnetic field, no induction would tke plce nd no torque cn be developed, so this condition is only found in idel no-lod situtions. When loded, reltive speed difference is required to mintin the induction effect, so synchronism or rotor slipping rises. This induction effect cn tke plce up to certin mximum, so the speed-torque rnge is not infinite. n cse of genertor opertion, oversynchronism occurs. n Fig. 3.5 squirrel cge rotor winding is represented by concentrted equivlent three-phse winding. n the figure, index denotes the sttor quntities nd index ll quntities relted to the rotor. w is the number of turns of the winding phse, m the number of phses nd ζ is the resulting winding fctor for the fundmentl frequency f, representing the flux wekening due to the distributed coils of the winding. Here, the three winding phses re nmed U, V nd W. The frequency eqution for the rotting mchine cn be written by: ω = ω + pω f = f + f mech (3.) Ωt f, m, w, ξ U f, m, w, ξ W U n V V W Figure 3.5: Rotor nd Sttor System of n nduction Mchine. Using the definition of the slip eq. (3.) rerrnges (3.) to: n n f f s = n f = = (3.3) nd yields the determintion of the slip-frequency for the rotor electric circuit: f f f = s (3.4) f To understnd the function nd to determine the opertionl behviour of the mchine, the induction mchine cn be understood s mgneticlly coupled system of two winding systems with different frequency. The slip s fctor cn be used to crete n equivlent one-phse model (Fig. 3.6). - 0 RTO-EN-AVT-3

11 R X σ X' σ R' /s _ 0 ' U_ ' U_ X h s Figure 3.6: Single-Phse Equivlent Circuit Model for the nduction Mchine. The model prmeters re: R : sttor resistnce (cn often be neglected); X σ : sttor lekge inductnce, representing the prt of the mgnetic field which is not mutully coupled between rotor nd sttor (for instnce ssocited with end-winding flux); X h : min inductnce ssocited to the mutully coupled flux; Xσ : rotor lekge inductnce; R /s: rotor resistnce, representing rotor losses nd the electromechnicl energy on the shft; nd U /s: induced voltge in the rotor; in cse of squirrel cge this is short-circuit. With these ssumptions the voltge eqution for rotor nd sttor cn be given: U ' U s = R + ' R = s ' jx σ jx ' σ + ' jx + h jx 0 h 0 = 0 (3.5) Applying n energy blnce (Fig. 3.7) delivers the losses nd powers of the induction mchine. The internl electromgnetic torque cn be determined. supplying net P el sttor P supp P Fe ir gp P δ P J rotor P em P Fe P J P Fric,v P m shft Figure 3.7: Energy Blnce of n nduction Mchine (Snkey digrm). RTO-EN-AVT-3 -

12 The blnce delivers the ir gp power P δ = P J + P em (3.6) with P em ) = ( s P nd P δ J = spδ this yields the importnt rule of the splitting ir gp power: η P P ( s) P m em δ = < = (3.7) P el P δ P δ Note tht it is inevitble to hve rotor Joule losses s this is linked to the necessry induction of the rotor mgnetic field. With this rule it is obvious tht n induction mchine cn only be operted efficiently t low vlues of the slip. The sttionry speed-torque chrcteristic of n induction mchine operted t the grid cn be determined (Fig. 3.8). T, T k 0 s n 0 0 n T brking T k motor genertor Figure 3.8: Chrcteristic of nduction Mchines Operted t the Constnt Grid. One cn prove tht the strting behviour of the mchine depends on the rotor resistnce t the supply frequency. Vrious concepts nd shpes of brs re used nowdys (Fig. 3.9). Figure 3.9: Shpes of Squirrel Cge Rotor Brs. Typicl chrcteristics in the opertionl re of induction motors re collected in Fig Since ll the mgnetic field energy needs to be supplied from outside the mchine, it consumes rective power (low cosϕ). - RTO-EN-AVT-3

13 n[tr/s], cos ϕ, [A], η, s n 0 n cos ϕ T n η s T [Nm] Figure 3.0: Typicl nduction Motor Chrcteristics. 4.0 SYNCHRONOUS MACHNES 4. Field-Wound Synchronous Mchines Synchronous mchines with field winding re the lrgest electricl mchines nd minly used s genertors for electricl power in hydro, nucler power or therml power sttions to trnsform mechnicl energy to electricl energy. Synchronous mchines in stedy-stte re rotting t constnt speed, directly proportionl to the supply frequency (50/60 Hz). They re constructed with high voltge/current AC three-phse winding in the sttor, lso referred to s the rmture, nd DC excittion winding, supplied externlly, in the rotor. Thus, the rotting ir gp field nd the ligned rotor field re rotting t the synchronous speed (eq. (3.); s=0). With f =0 the frequency eqution is rewritten: ω = ω + p ω mech f = 0 + f (4.) Due to its vrible DC excittion, building up mgnetic field inside, the synchronous genertor is cpble to drw either lgging or leding rective power. This is very importnt feture for its opertion in electricity networks. The sttor of synchronous genertor crries winding, similr to the one used for induction mchines, directly connected to the grid. The rotor hs the field winding fed from n externl DC source vi slip rings or rotting rectifier fed by three-phse excittion genertors mounted to the shft of the synchronous genertor. The lrgest sizes of genertors up to.8 GVA re found for 4-pole turbo mchines nd. GVA for the -pole vrint. Slow speed genertors for hydro power sttions with p = hve serve power rnge of up to 800 MVA. A specil clss of mchines of few MVA for (gerless) wind turbines exists s well. There re two different rotor constructions to distinguish: High speed mchines with cylindricl rotor, in slots distributed field winding nd uniform ir gp (turbo mchines); nd Low speed genertors with slient pole construction, concentrted field winding. The rotor shpe cn be either cylindricl or with slient poles (Fig. 4.). This hs consequences for the shpe of the induced voltge nd the control prmeter, s the inductnce in the direction of the field my differ from the inductnce in the qudrture direction. Cylindricl rotors re fbricted in one piece nd RTO-EN-AVT-3-3

14 re minly found in mchines for high speeds (<3 krpm). Lrge, slow mchines, re often of the slient pole type s they re constructed pole by pole (e.g. huge hydro genertors). slient pole mchine turbo mchine V U n 0 n 0 W V U n 0 n 0 W W U V W U V Figure 4.: Rotor Vrints of Synchronous Genertors. Due to the lrge dimensions of the coils of the synchronous genertor, eddy currents cn occur s the skin depth t fundmentl frequency is smller thn the size. Here specil winding rrngements, constructed s twisted brs, the Röbel brs, re required (Fig. 4.). To trnsmit the copper losses out of the mchine direct coil cooling is pplied (Fig. 4.). Figure 4.: Winding Arrngement (Röbel Brs) for Synchronous Genertors. f DC current f is pplied to the field winding of the synchronous genertor, sinusoidl distributed flux is estblished in the ir gp. The rottion of the shft, e.g. by stem turbines, results in revolving field in the ir gp. Due to the three-phse winding rrngement symmetricl voltge system is creted. The generted voltge is proportionl to the mchine s speed nd the exciting flux tht depends on the excittion current f. The frequency of the voltge is obviously proportionl to the mechnicl speed s well. f = p n (4.) To void trnsients nd high switching currents, severl conditions must be fulfilled before the synchronous genertor cn be switched to the grid. n prticulr, these re: phse sequence voltge - 4 RTO-EN-AVT-3

15 frequency phse f such conditions re not fulfilled, high trnsients cn occur nd dmge the mchine. First the phse sequence must be controlled nd eventully corrected. The synchronous genertor must then be strted. This is usully supported by strt-up motor. Very close to the synchronous speed, the excittion current is djusted yielding the desired mgnitude for the voltge. The frequency must now be djusted by very slowly chnging the speed of the drive, nd when the phse between mchine nd grid re in prllelism, the mchine cn be connected to the grid. To understnd the fundmentl behviour of the synchronous genertor the sttor voltge eqution: U R + j( X + X = E (4.3) σ h + ) for the turbo genertor is used. E is the excittion voltge (emf) nd U i is the voltge generted by the resulting ir gp field (Fig. 4.3). The rotor voltge eqution, in DC, cn be given by: U = R (4.4) b b b X h X σ R ~ E U i U Figure 4.3: One-Phse Equivlent Circuit for the Synchronous Mchine with Uniform Air Gp. With this one-phse model it is now possible to drw the phsor-digrm of the mchine. E [V] E jx h. U i jx. σ no-lod chrcteristic E = f( ) b R. ' θ U Ψ ϕ µ µ ' [A] Figure 4.4: Phsor-Digrm of Turbo Genertor in Opertion for Leding Rective Power. RTO-EN-AVT-3-5

16 For simplifictions nd to more esily derive the opertionl chrcteristics of synchronous genertor in the following discussion, the sttor resistnce is neglected. The cylindricl mchine nd the slient pole mchine re treted seprtely. By using the phsor-digrm of the turbo genertor with cylindricl rotor the voltge reltion cn be determined by trigonometriclly mnipultions. X..cosϕ ϕ jx X..cos ϕ = E.sinθ E θ U ϕ.cos ϕ = E X.sinθ Figure 4.5: Simplified Phsor Digrm for the Turbo Genertor. The synchronous torque cn directly be derived from the energy eqution: This yields P = ω T = P 3U cosϕ (4.5) = mech elec line mu cosϕ T = (4.6) ω reltion for the torque, depending on the terminl quntities nd the phse ngle of the mchine. Rerrnged nd using the excittion voltge it cn be written: mue T = sinθ = T sinθ (4.7) mx ω X With θ the lod ngle, to be interpreted s the ngle between the mgnetic field link to the rotor winding nd the mgnetic field linked to the sttor. This expression indictes tht there is mximum lod ngle, 90, so mximum torque of the mchine. t cn be shown tht if θ<90, the mchine is stble (Fig. 4.6). - 6 RTO-EN-AVT-3

17 T [Nm] motor T mx genertor π - - π T N stble stble θ N π π θ T mx Figure 4.6: Torque versus Power-Angle of the Turbo Genertor. For the slient pole genertor vrint the mgneticlly nisotropic rotor geometry is used to derive the torque chrcteristic. The equtions re trnsformed into d/q-xis system (Fig. 4.7) to determine the influence of the non-uniform ir gp on the mchine behviour. The index d stnds for the direct xis nd q for the qudrture xis of this co-ordinte system. U W Θ Θ q ϕ V Θ d θ V ψ W U Figure 4.7: d/q Axis System for the Rotor of the Slient Pole Genertor. The flux density distribution illustrtes the influence of the non-uniform ir gp (Fig. 4.8). RTO-EN-AVT-3-7

18 direct xis sttor qudrture xis sttor Θ d rotor rotor Θ q B d B q B d B q Figure 4.8: Air Gp Field Distribution in d nd q Axis of the Genertor with Slient Poles. The fundmentl of the flux density distribution, yielding the induced voltge (Fig. 4.7), cn be clculted by using the d/q field fctors: B B d q = C B d = C B q (4.8) The fctors cn be found in the rnge of C d = 0.8,, 0.9 nd C q = 0.4,, 0.5. The trnsformtion for the rectnces/inductnces (Fig. 4.9) into the d/q co-ordinte system cn be performed by using X X d q = X = X σ σ + C d + C X q X h h (4.9) E jx d d jx θ q q q U d ϕ ψ Figure 4.9: Phsor-Digrm. The voltge eqution E = U + jx + jx (4.0) q q d d - 8 RTO-EN-AVT-3

19 with the currents d q = sin Ψ = cos Ψ (4.) yields the desired torque chrcteristic for the slient pole synchronous mchine: m U. E U T =..sinθ +..sin θ (4.) ω X d X X q d t cn be noticed tht the torque consists of two components, synchronous torque T nd component cused by the symmetry of the rotor, reluctnce torque T double the power-ngle dependent (Fig. 4.0). Due to the reluctnce torque the stbility rnge of this genertor is decresed in this cse. T T 0 T π π θ Figure 4.0: Torque Chrcteristic of Slient Pole Synchronous Genertor. Dependent on the ctive nd rective current j = ϕ e = ( cosϕ jsinϕ ) E = sinθ + X (ctive current) E cosθ U X (rective current) (4.3) of synchronous mchine its working cn be distinguished in four qudrnts (Fig. 4.). RTO-EN-AVT-3-9

20 jx jx E θ ϕ U P > 0 E U θ ϕ Q < 0 Q > 0 jx U jx P < 0 U θ E ϕ θ E ϕ Figure 4.: Working Rnge of Synchronous Genertors. Due to the possibility of introducing DC current in the field winding nd due to the fct tht the mchine is connected to the grid, the excittion current determines the point of opertion. The mchine is cpble to supply the grid with cpcitive or inductive currents. The V-curves illustrte the possible working rnge for this opertion. They represent the lines of constnt ctive power. t must be noticed tht the genertion or consumption of rective power is independent from the mechnicl power of the mchine. stbility rnge 00 % b< b mx 75 % inductive opertion 50 % cpcitive opertion P =0 cos ϕ = no-lod b0 b Figure 4.: V-curves (curves of constnt ctive power) of Synchronous Genertor. The limittions for the working rnge re given by the π mximum lod ngle θ - 0 RTO-EN-AVT-3

21 mximum mechnicl power N cosϕ TN m. U ω N N, phse mximum excittion current < b b mx mximum sttor current < N Figure 4.3 shows these limittions in digrm for constnt excittion. Re U N,phse () () θ -j Ee jθ N X ϕ N N (3) -m U j N,phse N X (4) () Figure 4.3: Limittions of the Working Rnge of Synchronous Genertors. Often the rotors of lrge synchronous mchines re equipped with smll squirrel-cge, the dmper cge, to stbilize the mchine in cse of lrge trnsients nd/or to strt up the mchine. 4. Permnent Mgnet Motors For smller synchronous mchines, it becomes more dvntgeous to the use permnent mgnets to generte the rotor field (Fig. 4.4). The bove derived equtions nd behviour stys vlid, with the limittion tht the vrible excittion is to be replced by fixed term. PMSM: L d < L q β q d θ = ω r dt c' ω r b' α b ' c Permnent Mgnets Figure 4.4: Permnent Mgnet Synchronous Mchine with Surfce Mgnets. RTO-EN-AVT-3 -

22 Severl different constructionl vrints exist, differing in the positioning of the mgnets: for instnce, surfce mounted or embedded. Depending on the rotor construction, which determines X d nd X q, the reluctnce torque cn be positive or negtive. The used mgnets re usully powerful NdFeB mgnets. Often n extr bndge, e.g. fibre-glss, is necessry to keep the mgnets in position. Fig. 4.5 shows n exmple if PMSM with surfce mounted mgnets. Figure 4.5: PMSM Rotor nd Sttor nd Encoder. Such mchines exist in rnge up to 0 kw, with speeds up to 0 krpm. The min ppliction for such mchines is robotics (servo-drives), but new mrkets, e.g. hybrid electricl vehicles nd microturbines, rise. These mchines cnnot be run off the grid (no dmper cge) nd need to be supplied from power electronic converter, supplying the correct frequency. Such frequency converter my supply sinusoidl voltge wveform or squre-wve voltge, with mny hrmonics. This simpler supply hs disdvntges in terms of noise nd losses, but comes with simpler voltge inverter with much lower switching frequency. Such squre-wve voltge supplied PMSM is known s Brushless-DC mchine (BLDC) or Electroniclly Commutted DC-mchine due to its nlogy is opertion to DC-mchine, but considered inside-out. Becuse of the limited number of switchings per electricl period (six), high fundmentl frequency cn be generted, mking this chep drive for high speeds (few 0 krpm). 4.3 Switched Reluctnce nd Stepper Motors Synchronous mchines cn be operted on reluctnce forces s well. n generl this yields robust simple mchines s no rotor windings nor mgnets re involved. Two types of such reluctnce-bsed synchronous mchine re populr: 4.3. Switched Reluctnce Mchine A switched-reluctnce mchine (SRM) contins solid rotor with series of poles. The sttor is not built with distributed winding in slots, but uses concentrted poles. To be ble to generte torque in ny position, these pole numbers must not be different. The sttor pole pirs re exited one-by-one, mking the rotor follow. Hence single-phse power electronic circuit per sttor pole pir is required. - RTO-EN-AVT-3

23 Figure 4.6: Exmple of n SRM, with the Connections for One Sttor Pole Visible. As these mchines re very simple nd robust nd cn be mde quite efficient, they gin populrity. t is possible to use them s high-speed mchine Stepper Motor The stepper motor cn be considered the smll brother of the SRM. t lso works on reluctnce torque, but in generl hs mny more rotor poles. The purpose of this smll mchine (power: few W or tens of W) is positioning in smll robotics pplictions: by putting current pulse on pole, the motor jumps to the next stble positions. Sometimes mgnet is present for holding torque. Figure 4.7: Stepper Motor Cross-Section. 5.0 ELECTRCAL DRVES Nowdys, n electricl mchine is often not operted on its own. t is just piece broder system (Fig. 5.), clled drive, together with: the lod; sensors, such s encoders, trnsducers; power electronics for the motor; the controller(s); nd trnsmission system. RTO-EN-AVT-3-3

24 demnd controller power electronics motor trnsmission system lod sensors sensors Figure 5.: Block Digrm of Typicl Drive System. The power electronics nd motor usully re considered s integrl pckge. n order to select the pproprite system elements, vrious dt hve to be collected. Tble 5. shows collection of the most importnt ones. Tble 5.: System Requirements to be Considered during Selection of Elements for Drive System lod environmentl spects life-cycle costs system integrtion speed ccelertion & decelertion motion profile dynmic requirements forces, torque sfety EMC spects climtic nd humidity rnges supply specifictions electricl comptibility initil costs opertionl costs mintennce costs disposl costs mechnicl fitting bering nd couplings cooling comptibility with existing systems One of the min design decisions tht hve to be tken, is the selection of n pproprite motor technology for the requirements of the prticulr ppliction. For instnce, Tble 5. shows the requirements of servo drive in robotics. With the rpid development in this field, number of options re vilble. Ech option will hve benefits nd disdvntges. n the considertion of the entire drive, the motor determines the drive s chrcteristic. Furthermore, the motor determines the selection of the power electronic converter nd the control requirements. - 4 RTO-EN-AVT-3

25 Tble 5.: Requirements of Servo Drive high rtio speed/torque four-qudrnt opertion high torque t stndstill high overlod cpbility low torque ripple quiet opertion high rtio power/weight high system relibility A wide rnge of possibilities exists. However, only limited number of combintions will hve the chrcteristic necessry. Possible cndidtes for the ppliction in Tble 5. could be: Brushed, permnent mgnet, direct-control DC motor equipped with PWM controller; Brushless, permnent mgnet, DC motors; Vector or flux controlled AC induction motors; nd Stepper motors. With the exception of the brushed DC motor, ll others re totlly depending on their power electronic converter. Therefore, they re to be treted s integrted drives. Fig. 5. shows the vrious possibilities for the selection of the drive elements. From this figure, it is obvious tht the entire drive consists of the five elements shown in Fig. 5.. powersupply EMC control powerelectronic motor Ω, T lod µp gte rry C logic GBT trnsistor Mosfet Comfet Tric GTO HVC dc (fieldwindg.) dc (PM) dc (brushless) SR ASM SYM smrtpower steppermotor Figure 5.: Overview of Possible Drive Systems. As mentioned, the selection of the pproprite components of the drive system hs to be done very crefully. This cn be considered to require the collection of dt nd its detiled nlysis. The design prmeters of the mechnicl trnsmission system of e.g. mchine-tool drive must be identified t the erliest possible stge. t must be relised tht the entire system will be subjected to detiled design chnges s development proceeds. The selection of the motor, its mechnicl system, the required power RTO-EN-AVT-3-5

26 electronic nd control strtegy is by necessity n itertive process. Any solution is compromise. To be ble to select the pproprite components of the system, structured wy of mking decisions is required. Therefore, the bsic principles nd function of combintions of the components hve to be known. Tble 5.3 collects the bsic combintions of electricl motors combined with the required of power electronic circuits. Tble 5.3: Schemtic of Typicl Power Electronic Converters for Vrious Motor Applictions self-led motors externl-led motors type motor universl-motor PM- (fieldwinding) EC- (PM-rotor) synchronous motor synchronous motor mixed voltge motor DCvoltge motor PM SRM stepper motor speed control gtin control ~ PWM ~ ~ - switching logic rotor position sensor - gting control ~ PWM ~ switching logig ~ ~ M M M ~ M Steuerelektronik RG M Steuer elektroni M M n generl, once the overll ppliction, the speed nd torque requirements re identified; vrious combintions cn be selected to form the first step of the drive development itertion. Further selections of combintions my be done compring benefits nd disdvntges nd then by using the mnufcturer s specifictions nd dt sheets yielding in second phse detiled rnking of the combintions. Here, vlution by computer simultions is commonly used to vlidte the selected combintions. Some bsic selection considertions re: Strt-up condition: The pek torque required by the lod ppliction must be less thn both, the stll torque of the motor nd the pek torque of the motor, which cn be produced with the power electronic chosen. Rted opertion: The root-men-squre (rms) torque required by the lod ppliction must be less thn both, the rted torque of the motor nd the rted torque of the motor, which cn be produced with the power electronic chosen. To ensure opertion even t voltge fluctutions in the supply: The mximum speed required by the lod ppliction must not be higher thn pproximtely 80% of the mximum no-lod speed of the motor-power electronic combintion. The opertion regime hs to be studied when motor nd its ssocited power electronic converter re selected. n generl, two types of opertionl duty lod pplictions cn be distinguished: continuous or intermittent: For the continuous lod duty, the time for ccelerting nd decelerting the drive is not criticl. The mximum required torque (externl lod plus the drive-trin s friction) hs to be provided on - 6 RTO-EN-AVT-3

27 continuous bsis. The pek torque nd the verge torque requirements re not significntly different when compred to the continuous torque. Motor nd controller re chosen primrily considering the mximum speed nd continuous torque requirements. n contrst to the continuous lod duty ccelertion nd decelertion of the lod forms significnt prt of the motor s duty cycle t opertion t intermittent duty. n this cse the entire inerti of the moving system (motor + lod) must be considered when the ccelertion torque is being determined. Therefore, the ccelertion torque, the friction torque nd ny dditionl continuous lod torque present during ccelertion must be exceeded by the pek torque cpbility of the integrl drive. n ddition, the drive s continuous torque cpbility must exceed the required verge torque resulting from the worst-cse positioning move. The considertions mde re illustrting tht detiled nlysis of the overll mechnicl drive system is required for the design. Whtever motor is chosen for the system, the dynmic reltionships within the mechnicl drive system re fundmentl to the system selection nd hve to be considered in n erly stge of the design. RTO-EN-AVT-3-7

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