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# ELECTRIC POWER EE 3410

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This 38 page Class Notes was uploaded by Kenya Rutherford on Tuesday October 13, 2015. The Class Notes belongs to EE 3410 at Louisiana State University taught by E. Mendrela in Fall. Since its upload, it has received 22 views. For similar materials see /class/223163/ee-3410-louisiana-state-university in Electrical Engineering at Louisiana State University.

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Date Created: 10/13/15

EE 7 3410 Electric Power Fall 2003 Instructor Ernest Mendrela Generation of Electrical Energy 1Fundamentals on generation of the voltage and mechanical force torque l 1 Linear system Fig1l illustrates the generation of electromotive force EMF voltage e and mechanical force F Symbols B 7 magnetic ux density P 7 magnetic ux i 7 current v speed Fig1l Generation of a EMF e right hand rule b force F left hand rule Fig 12 shows linear machines Where in Fig1 2b is illustrated the generation of EMF e in Fig12b 7generation ofmechanical force F and in Fig12c 7 linear generator Where the both e and F are produced if the Winding circuit consisting of N turns is closed through the load impedance 2 a EBvlNeN 03 CD39 i H N 2 FBilN w c E eN generator E gt V d E lt V motor Fig12 Linear electric machines a generation of voltage 2 b generation of force F c linear generator d linear motor 12 Rotary system Twopole machine with a single coil phase is shown in Fig13 The rotor with permanent magnets rotates at speed com It induces the electromotive force 2 EMF a b Singlecoil stator Winding perm anth magnet salientpole rotor Coil Av A2 Fig13 Cylindrical machine with a singlecoil and permanent magnet rotor a machine b coil changing sinusoidally with respect to the rotor position p Fig14a and sinusoidally in time Fig14b according to the function eE n sinmt 1 where ca27rf and a 2pcom a b e EMF 7r2 7t 27 a Pole pitch Fig14 Voltage induced in the coil a as a function of rotational angle b as a function of time If the coil is supplied by the current i the force electromagnetic torque T6quot is produced The direction of force acting on the coil is opposite to the force electromagnetic torque Tem acting on the rotor Fig 15 Force F electromagnetic torque Tem developed in the motor 2 Three phase synchronous generator 21 Construction and principle of operation The 3phase synchronous machine is shown in Fig21 It consists of two parts stator and rotor Both stator and rotor have windings The stator winding is a 3phase winding and is sometimes called the armature winding The rotor winding is called the eld winding which is connected to dc supply through the slip rings and brushes There are two types of rotors o Salientpole rotor Fig21a 7 for lowspeed machines eg hydrogenerators o Cylindrical rotor Fig21b 7 for highspeed machines eg turbogenerators a 3phase stator winding rotor eld winding b 3phase stator winding cylindrical rotor rotor field winding Fig21 Construction scheme of synchronous machine with a salientpole rotor b cylindrical rotor The cylindrical rotor has one distributed winding and an essentially uniform air gap The salient pole rotors have concentrated windings on the poles and a nonuniform air gap 211 Synchronous generators When the eld current ows through the rotor eld winding it establishes a sinusoidally distributed ux in the air gap If the rotor rotates the rotating magnetic eld induces voltages in the stator windings Since the threephase windings are shifted by 120 angle from one another the induced so called excitation voltages are shifted in time from one another by the angle of 120 Fig22 6 1 Efm sinat eB Efm sinat 120 7 21 ec Efm sinat 2400 Fig22 Waveforms of 3phase voltages induced in the armature winding of the synchronous generator The rms excitation voltage in each phase is Efm E 444f fNKW 22 Fe Pf is the magnetic ux due to the excitation current N is the number of turns in each phase Kw is the winding factor where The frequency of the induced voltage is related to the rotor speed by 23 P f 0 24 where n is the rotor speed in rpm p is the number of poles 212 Synchronous motors If the synchronous machine operates as a motor the 3phase armature winding is connected to 3phase ac supply The stator currents produce the rotating magnetic ux The eld winding connected to dc source produces the magnetic ux steady with respect to the rotor To produce the torque these two magnetic uxes cannot move with respect to one another It means that the rotor should rotate with the same speed as the rotating ux produced by the stator Fig23 When the machine operates as a generator the rotor is driven by the external machine and the stator rotating eld follows the rotor being shifted with respect to the rotor by the angle 639 Fig23a When operating as the synchronous motor the rotor follows the stator rotating field by the angle 9 Fig23b The motor at zero rotor speed does not develop any torque To make the motor operate the rotor should reach first the synchronous speed The methods of starting the synchronous motor will be discussed later a b pf a 5 S 7 lt Inf 9 Fig23 Explanation to the operation of a synchronous generator and b synchronous motor In the following sections first the steadystate performance of the synchronous machine with cylindrical rotor and unsaturated magnetic circuit will be studied Then the effect of saliency in the rotor poles will be considered 22 Equivalent circuit model The equivalent circuit will be derived on a perphase basis The current If in the field winding produces the Qf ux The current Ia in the stator produces ux 45 Part of it Pas known as the leakage ux does not links with the field winding A major part 45 known as the armature reaction ux links with the field winding The resultant air gap ux d5 is therefore due to the two components uxes Qf and Q Each component ux induces a component voltage in the stator winding qu gt E f dDm gt Em 05 a E05 and the resultant ux d3 gt E The excitation voltage Ef can be found from the open circuit curve of Fig24 However the voltage Ea known as the armature reaction voltage and the voltage Em depend on armature current Therefore they can be presented as the voltage drops across the reactances X 7 reactance of a1mature reaction and Xas 7 leakage reactance This is shown in the equivalent circuit of a synchronous machine only stator circuit is considered in Fig25a Eft 0 If Fig24 Opencircuit characteristic of the synchronous generator a 121 X 211quot X215 R21 Ef E V zL b 12 Xs R NW 4 VAV Bf D V 2L c Bf D V 12L Fig25 Synchronous machine equivalent circuit a armature reaction reactance X armature leakage reactance X b synchronous reactance Xx c armature impedance Zs The relations between these voltages are as follows EEr m 25 or E E ma 26 The voltage equation for the whole circuit is Fig25a KEf Ra a JXmia JXmla 27 or Fig25b ZEf Rala JXSL 28 or Fig25c ZEf Zsla 29 where X S X m Xas synchronous reactance ZS Ra 1X synchronous impedance The phasor diagram for generator and motor operation is shown in Fig26 The terminal voltage is taken as the reference phasor The angle 6 between Vand Ef known as the power angle is positive for generating action and negative for the motoring action This angle referred to the mutual position of field winding ux and armature winding ux is shown in Fig23 In generating operation the rotor ux f the rotor is driven by the external machineturbine is pulling the stator ux and the angle 6 is positive while in motoring operation the stator ux 1 is pulling the rotor 20 b P Fig26 Phasor diagrams for a synchronous generator with the armature resistance Ra and b without Ra c synchronous motor with the armature resistance Ra and d without Ra 23 Power and torque characteristics The complex power at the terminals is SmVI The stator current from the equivalent circuit Fig25c 1 2EV a Z Z Z Pall 5 IVIZO Zs 4w Z 4w z S 6 z s IVHEfl IVI2 SMWZ 5 ZS 4 S m lVllEflcosgp 5 IVIZ cosgp ZS S ZS S S m Msin p 5 IVIZ singp IZSI s ZS s 210 211 212 213 214 11 In large synchronous machines Ra ltlt Xx thus Z S XS and S 90quot From the above equations P mwsiME 215 IZ Z s 2 lVllEfl 1V1 Q m cos5 216 ZS The Eq215 can be directly derived from the phasor diagram drawn for Ra 0 Fig26b and d In general the active power PmVIa cosgo 217 and reactive power QmVIa sinqp 218 From the phasor diagram the section 0 EXslacosgmor 219 o EEfsingo 220 From these two formulae XSLZ cosgpEfsin5 and 221 Ef In cosgp Ysin 222 Combining Eq222 and 217 we get VF P m s1n5 223 X 5 Because the stator losses are neglected in this analysis the power developed at the terminals is also the air gap power The torque developed by the machine is T 224 a s Inserting Eq223 to 224 VF s1n5 225 X s m T a The torquepower angle characteristic drawn at V const and If const is shown in Fig27 The maximum torque known also as the pullout torque is at 639 90quot The machine will lose synchronism if 6 gt 90quot The pullout torque can be increased by increasing the excitation current If max n2 11 3 generator Fig27 Torquepower angle characteristic 24 Power factor control Looking at phasor diagram we see that E X310 cosqp m P and 226 5 X310 sinqm Q 227 If the synchronous machine is connected to the system with V const and f const and the power on the rotor shaft P const then changing the eld current If the induced voltage Ef changes too and the locus of the voltage Ef Fig28 is the horizontal line p pointA slides onp line At the same time the current Ia changes too and its locus is also straight line i perpendicular to phasor V When the eld current changes the section CB which symbolizes the reactive power Q changes too For the low eld current If point A1 the reactive power is capacitive the stator current Ia is large and leading This state is called underexcitation Elfl EfZ Ef3 A1 A2 A3 P A P 1212 V W 1213 Qc Qi i Fig28 Operation of synchronous generator at constant active power P and constant voltage and frequency At point A 2 the eld current is equal Ifz the armature current is minimum Liz and is in phase with voltage VPF 1 and the reactive power Q section 5 is zero This state is called normal excitation For larger eld current If If3 point A3 the stator current 13 is large again and is lagging and the reactive power Q is inductive I a PF PE 0 inductive load 0 If underexcitation overexcitation Fig29 Vcurves characteristics of machine operating at constant voltage V and frequency 14 The variation of the stator current with the eld current for constantpower operation is shown in Fig29 The set of characteristics drawn for different power are known as V cnrves because of their shape The variation of the power factor with the eld current dashed curves are inverted Vcnrves This feature of the power factor control by the field current is utilized to improve the power factor of a plant If the synchronous machine is not transferring any power but is simply oating on the infinite bus the power factor is zero The stator current either leads or lags the stator voltage by 90quot Fig210 The magnitude of the stator current changes as the field current is changed but the stator current is always reactive The machine behaves like a variable inductor or capacitor as the field current is changed Therefore the unloaded synchronous machine is called a synchronous condenser and may be used to regulate the receivingend voltage of a long power transmission line a b Ala Ef O A Ef A XSIa V XSIa 0 V W4 HF Q Qc Ia Fig210 Operation of the synchronous machine as a synchronous condenser machine deliver to the load in nite bns a capacitive reactive power b inductive power 25 Operation of synchronous machine as an independent generator Synchronous machines are normally connected to an infinite bus However small synchronous generators may be required to supply independent electric loads As an example a gasoline engine can drive the synchronous generator at constant frequency In such a system the terminal voltage tends to change with varying load To determine the terminal characteristics of an independent synchronous generator consider the equivalent circuit in Fig2ll At open circuit V Ef Ia 0 and at short circuit V 0 Ia I EXS If the load current is changed from 0 to I the terminal voltage Vwill change from Ef to zero Fig212 illustrates these changes in form of VI characteristics drawn for various PF of the load For the purely reactive load ZEfJXSL 28 and from the phasor diagram the straight line VI characteristic is concluded for pure inductive and pure capacitive load 13 XS NY 39 Fig2 11 Equivalent circuit of synchronous generator operating on the load Z L V Er Fig212 VI characteristics of synchronous machine operating as an independent generator 26 Salient pole synchronous machine Low speed multipolar synchronous machine has salient poles and nonuniform air gap Fig2l3 The magnetic reluctance is low along the poles tiaxis and high between poles qaxis If the ux Du produced by the armature stator current is aligned with d aXis the current Ia experiences reactance XM Such a reactance experiences the stator 16 current for cylindrical rotor independently on the rotor position with respect to stator ux Q When the stator ux takes the position parallel to the qaxis the armature reaction reactance for the stator current is Xaq smaller than XM Thus the armature reaction reactance changes vs power angle Jas is shown in Fig2l4 Ad Fig2l3 Armature reaction magnetic ux Du of synchronous machine with salient poles directed along qwcis Xa Ah Xad Xaq 00V 7c2 TE Fig2 14 Variation of armature reaction reactance Xa along the stator circumference of the salient pole synchronous machine 17 When the power angle varies the mutual position of stator ux and the rotor the unexcited rotor experiences the torque called reluctance torque what illustrates Fig215 This torque changes according to equation 2 Z 1V L i sin25 229 ms 2 Xq Xd The excited salient synchronous machine develops the resultant torque that is the sum of electromagnetic torque and reluctance torque VE V2 1 1 T fsm5 s1n25TmZ 230 ms XS ms 2 Xq Xd T A T TEm TR max I l TEm I I x39n o x 7t2a f7 5 motor generator Fig215 Torquepower angle characteristics of synchronous machine with salientpole rotor The torquepower angle characteristics drawn at different excitation currents and constant terminal voltage V are shown in Fig2l6 For salient pole machine the eld current may be reduced to zero and the reluctance torque can keep machine still in synchronism Fig2l6 Torquepower angle characteristics of synchronous machine with salientpole rotor at various eld currents 27 Connection of a synchronous generator to the in nite bus Synchronous generators are rarely used to supply the individual loads These generators in general are connected to a power system known as an in nite bus or grid The voltage and frequency of the in nite bus hardly change The operation of connecting a synchronous generator to the in nite bus is known as paralleling with the in nite bus Before the generator can be connected to the in nite bus the incoming generator and the in nite bus must have the same 0 Voltage 0 Frequency 0 Phase sequence 0 Phase In the power plant the satisfaction of these conditions is checked by an instrument known as a synchronoscope Fig2l7 illustrates the situation when one of the above mentions quantities are not equal 1 Rms voltages are not the same but frequency and phase sequence are the same Fig2 l7a 2 Frequencies are not the same but voltages and phase sequences are the same Fig2l7b 3 Phase sequences are not the same but voltages and frequencies are are the same Fig2l7c Phase is not the same but voltage frequency and phase sequence are the same Fig2l7d 4 V a c Fig2l7 Phasor diagrams illustrating the situation when one of the conditions for equal instantaneous generator and infinite base voltages are not met Each case mentioned above causes the voltage difference across the switch between generator and in nite bus terminals and if are connected it will produce a disastrous situation for the generator EE 7 3410 Electric Power Fall 2003 Instructor Ernest Mendrela Generation of Electrical Energy 1Fundamentals on generation of the voltage and mechanical force torque l 1 Linear system Fig1l illustrates the generation of electromotive force EMF voltage e and mechanical force F Symbols B 7 magnetic ux density P 7 magnetic ux i 7 current v speed Fig1l Generation of a EMF e right hand rule b force F left hand rule Fig 12 shows linear machines Where in Fig1 2b is illustrated the generation of EMF e in Fig12b 7generation ofmechanical force F and in Fig12c 7 linear generator Where the both e and F are produced if the Winding circuit consisting of N turns is closed through the load impedance 2 a EBvlNeN 03 CD39 i H N 2 FBilN w c E eN generator E gt V d E lt V motor Fig12 Linear electric machines a generation of voltage 2 b generation of force F c linear generator d linear motor 12 Rotary system Twopole machine with a single coil phase is shown in Fig13 The rotor with permanent magnets rotates at speed com It induces the electromotive force 2 EMF a b Singlecoil stator Winding perm anth magnet salientpole rotor Coil Av A2 Fig13 Cylindrical machine with a singlecoil and permanent magnet rotor a machine b coil changing sinusoidally with respect to the rotor position p Fig14a and sinusoidally in time Fig14b according to the function eE n sinmt 1 where ca27rf and a 2pcom a b e EMF 7r2 7t 27 a Pole pitch Fig14 Voltage induced in the coil a as a function of rotational angle b as a function of time If the coil is supplied by the current i the force electromagnetic torque T6quot is produced The direction of force acting on the coil is opposite to the force electromagnetic torque Tem acting on the rotor Fig 15 Force F electromagnetic torque Tem developed in the motor 2 Three phase synchronous generator 21 Construction and principle of operation The 3phase synchronous machine is shown in Fig21 It consists of two parts stator and rotor Both stator and rotor have windings The stator winding is a 3phase winding and is sometimes called the armature winding The rotor winding is called the eld winding which is connected to dc supply through the slip rings and brushes There are two types of rotors o Salientpole rotor Fig21a 7 for lowspeed machines eg hydrogenerators o Cylindrical rotor Fig21b 7 for highspeed machines eg turbogenerators a 3phase stator winding rotor eld winding b 3phase stator winding cylindrical rotor rotor field winding Fig21 Construction scheme of synchronous machine with a salientpole rotor b cylindrical rotor The cylindrical rotor has one distributed winding and an essentially uniform air gap The salient pole rotors have concentrated windings on the poles and a nonuniform air gap 211 Synchronous generators When the eld current ows through the rotor eld winding it establishes a sinusoidally distributed ux in the air gap If the rotor rotates the rotating magnetic eld induces voltages in the stator windings Since the threephase windings are shifted by 120 angle from one another the induced so called excitation voltages are shifted in time from one another by the angle of 120 Fig22 6 1 Efm sinat eB Efm sinat 120 7 21 ec Efm sinat 2400 Fig22 Waveforms of 3phase voltages induced in the armature winding of the synchronous generator The rms excitation voltage in each phase is Efm E 444f fNKW 22 Fe Pf is the magnetic ux due to the excitation current N is the number of turns in each phase Kw is the winding factor where The frequency of the induced voltage is related to the rotor speed by 23 P f 0 24 where n is the rotor speed in rpm p is the number of poles 212 Synchronous motors If the synchronous machine operates as a motor the 3phase armature winding is connected to 3phase ac supply The stator currents produce the rotating magnetic ux The eld winding connected to dc source produces the magnetic ux steady with respect to the rotor To produce the torque these two magnetic uxes cannot move with respect to one another It means that the rotor should rotate with the same speed as the rotating ux produced by the stator Fig23 When the machine operates as a generator the rotor is driven by the external machine and the stator rotating eld follows the rotor being shifted with respect to the rotor by the angle 639 Fig23a When operating as the synchronous motor the rotor follows the stator rotating field by the angle 9 Fig23b The motor at zero rotor speed does not develop any torque To make the motor operate the rotor should reach first the synchronous speed The methods of starting the synchronous motor will be discussed later a b pf a 5 S 7 lt Inf 9 Fig23 Explanation to the operation of a synchronous generator and b synchronous motor In the following sections first the steadystate performance of the synchronous machine with cylindrical rotor and unsaturated magnetic circuit will be studied Then the effect of saliency in the rotor poles will be considered 22 Equivalent circuit model The equivalent circuit will be derived on a perphase basis The current If in the field winding produces the Qf ux The current Ia in the stator produces ux 45 Part of it Pas known as the leakage ux does not links with the field winding A major part 45 known as the armature reaction ux links with the field winding The resultant air gap ux d5 is therefore due to the two components uxes Qf and Q Each component ux induces a component voltage in the stator winding qu gt E f dDm gt Em 05 a E05 and the resultant ux d3 gt E The excitation voltage Ef can be found from the open circuit curve of Fig24 However the voltage Ea known as the armature reaction voltage and the voltage Em depend on armature current Therefore they can be presented as the voltage drops across the reactances X 7 reactance of a1mature reaction and Xas 7 leakage reactance This is shown in the equivalent circuit of a synchronous machine only stator circuit is considered in Fig25a Eft 0 If Fig24 Opencircuit characteristic of the synchronous generator a 121 X 211quot X215 R21 Ef E V zL b 12 Xs R NW 4 VAV Bf D V 2L c Bf D V 12L Fig25 Synchronous machine equivalent circuit a armature reaction reactance X armature leakage reactance X b synchronous reactance Xx c armature impedance Zs The relations between these voltages are as follows EEr m 25 or E E ma 26 The voltage equation for the whole circuit is Fig25a KEf Ra a JXmia JXmla 27 or Fig25b ZEf Rala JXSL 28 or Fig25c ZEf Zsla 29 where X S X m Xas synchronous reactance ZS Ra 1X synchronous impedance The phasor diagram for generator and motor operation is shown in Fig26 The terminal voltage is taken as the reference phasor The angle 6 between Vand Ef known as the power angle is positive for generating action and negative for the motoring action This angle referred to the mutual position of field winding ux and armature winding ux is shown in Fig23 In generating operation the rotor ux f the rotor is driven by the external machineturbine is pulling the stator ux and the angle 6 is positive while in motoring operation the stator ux 1 is pulling the rotor 20 b P Fig26 Phasor diagrams for a synchronous generator with the armature resistance Ra and b without Ra c synchronous motor with the armature resistance Ra and d without Ra 23 Power and torque characteristics The complex power at the terminals is SmVI The stator current from the equivalent circuit Fig25c 1 2EV a Z Z Z Pall 5 IVIZO Zs 4w Z 4w z S 6 z s IVHEfl IVI2 SMWZ 5 ZS 4 S m lVllEflcosgp 5 IVIZ cosgp ZS S ZS S S m Msin p 5 IVIZ singp IZSI s ZS s 210 211 212 213 214 11 In large synchronous machines Ra ltlt Xx thus Z S XS and S 90quot From the above equations P mwsiME 215 IZ Z s 2 lVllEfl 1V1 Q m cos5 216 ZS The Eq215 can be directly derived from the phasor diagram drawn for Ra 0 Fig26b and d In general the active power PmVIa cosgo 217 and reactive power QmVIa sinqp 218 From the phasor diagram the section 0 EXslacosgmor 219 o EEfsingo 220 From these two formulae XSLZ cosgpEfsin5 and 221 Ef In cosgp Ysin 222 Combining Eq222 and 217 we get VF P m s1n5 223 X 5 Because the stator losses are neglected in this analysis the power developed at the terminals is also the air gap power The torque developed by the machine is T 224 a s Inserting Eq223 to 224 VF s1n5 225 X s m T a The torquepower angle characteristic drawn at V const and If const is shown in Fig27 The maximum torque known also as the pullout torque is at 639 90quot The machine will lose synchronism if 6 gt 90quot The pullout torque can be increased by increasing the excitation current If max n2 11 3 generator Fig27 Torquepower angle characteristic 24 Power factor control Looking at phasor diagram we see that E X310 cosqp m P and 226 5 X310 sinqm Q 227 If the synchronous machine is connected to the system with V const and f const and the power on the rotor shaft P const then changing the eld current If the induced voltage Ef changes too and the locus of the voltage Ef Fig28 is the horizontal line p pointA slides onp line At the same time the current Ia changes too and its locus is also straight line i perpendicular to phasor V When the eld current changes the section CB which symbolizes the reactive power Q changes too For the low eld current If point A1 the reactive power is capacitive the stator current Ia is large and leading This state is called underexcitation Elfl EfZ Ef3 A1 A2 A3 P A P 1212 V W 1213 Qc Qi i Fig28 Operation of synchronous generator at constant active power P and constant voltage and frequency At point A 2 the eld current is equal Ifz the armature current is minimum Liz and is in phase with voltage VPF 1 and the reactive power Q section 5 is zero This state is called normal excitation For larger eld current If If3 point A3 the stator current 13 is large again and is lagging and the reactive power Q is inductive I a PF PE 0 inductive load 0 If underexcitation overexcitation Fig29 Vcurves characteristics of machine operating at constant voltage V and frequency 14 The variation of the stator current with the eld current for constantpower operation is shown in Fig29 The set of characteristics drawn for different power are known as V cnrves because of their shape The variation of the power factor with the eld current dashed curves are inverted Vcnrves This feature of the power factor control by the field current is utilized to improve the power factor of a plant If the synchronous machine is not transferring any power but is simply oating on the infinite bus the power factor is zero The stator current either leads or lags the stator voltage by 90quot Fig210 The magnitude of the stator current changes as the field current is changed but the stator current is always reactive The machine behaves like a variable inductor or capacitor as the field current is changed Therefore the unloaded synchronous machine is called a synchronous condenser and may be used to regulate the receivingend voltage of a long power transmission line a b Ala Ef O A Ef A XSIa V XSIa 0 V W4 HF Q Qc Ia Fig210 Operation of the synchronous machine as a synchronous condenser machine deliver to the load in nite bns a capacitive reactive power b inductive power 25 Operation of synchronous machine as an independent generator Synchronous machines are normally connected to an infinite bus However small synchronous generators may be required to supply independent electric loads As an example a gasoline engine can drive the synchronous generator at constant frequency In such a system the terminal voltage tends to change with varying load To determine the terminal characteristics of an independent synchronous generator consider the equivalent circuit in Fig2ll At open circuit V Ef Ia 0 and at short circuit V 0 Ia I EXS If the load current is changed from 0 to I the terminal voltage Vwill change from Ef to zero Fig212 illustrates these changes in form of VI characteristics drawn for various PF of the load For the purely reactive load ZEfJXSL 28 and from the phasor diagram the straight line VI characteristic is concluded for pure inductive and pure capacitive load 13 XS NY 39 Fig2 11 Equivalent circuit of synchronous generator operating on the load Z L V Er Fig212 VI characteristics of synchronous machine operating as an independent generator 26 Salient pole synchronous machine Low speed multipolar synchronous machine has salient poles and nonuniform air gap Fig2l3 The magnetic reluctance is low along the poles tiaxis and high between poles qaxis If the ux Du produced by the armature stator current is aligned with d aXis the current Ia experiences reactance XM Such a reactance experiences the stator 16 current for cylindrical rotor independently on the rotor position with respect to stator ux Q When the stator ux takes the position parallel to the qaxis the armature reaction reactance for the stator current is Xaq smaller than XM Thus the armature reaction reactance changes vs power angle Jas is shown in Fig2l4 Ad Fig2l3 Armature reaction magnetic ux Du of synchronous machine with salient poles directed along qwcis Xa Ah Xad Xaq 00V 7c2 TE Fig2 14 Variation of armature reaction reactance Xa along the stator circumference of the salient pole synchronous machine 17 When the power angle varies the mutual position of stator ux and the rotor the unexcited rotor experiences the torque called reluctance torque what illustrates Fig215 This torque changes according to equation 2 Z 1V L i sin25 229 ms 2 Xq Xd The excited salient synchronous machine develops the resultant torque that is the sum of electromagnetic torque and reluctance torque VE V2 1 1 T fsm5 s1n25TmZ 230 ms XS ms 2 Xq Xd T A T TEm TR max I l TEm I I x39n o x 7t2a f7 5 motor generator Fig215 Torquepower angle characteristics of synchronous machine with salientpole rotor The torquepower angle characteristics drawn at different excitation currents and constant terminal voltage V are shown in Fig2l6 For salient pole machine the eld current may be reduced to zero and the reluctance torque can keep machine still in synchronism Fig2l6 Torquepower angle characteristics of synchronous machine with salientpole rotor at various eld currents 27 Connection of a synchronous generator to the in nite bus Synchronous generators are rarely used to supply the individual loads These generators in general are connected to a power system known as an in nite bus or grid The voltage and frequency of the in nite bus hardly change The operation of connecting a synchronous generator to the in nite bus is known as paralleling with the in nite bus Before the generator can be connected to the in nite bus the incoming generator and the in nite bus must have the same 0 Voltage 0 Frequency 0 Phase sequence 0 Phase In the power plant the satisfaction of these conditions is checked by an instrument known as a synchronoscope Fig2l7 illustrates the situation when one of the above mentions quantities are not equal 1 Rms voltages are not the same but frequency and phase sequence are the same Fig2 l7a 2 Frequencies are not the same but voltages and phase sequences are the same Fig2l7b 3 Phase sequences are not the same but voltages and frequencies are are the same Fig2l7c Phase is not the same but voltage frequency and phase sequence are the same Fig2l7d 4 V a c Fig2l7 Phasor diagrams illustrating the situation when one of the conditions for equal instantaneous generator and infinite base voltages are not met Each case mentioned above causes the voltage difference across the switch between generator and in nite bus terminals and if are connected it will produce a disastrous situation for the generator

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