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This chapter include all of the following content: Introduction to polyphase synchronous machines, synchronous – machine inductances and equivalent circuits, performance characteristics, effects of salient poles, power – angle characteristics of salient – pole machines, permanent – magnet ac motors.
Nguyễn Công Phương ELECTROMECHANICAL ENERGY CONVERSION Synchronous Machines Contents I Magnetic Circuits and Magnetic Materials II Electromechanical Energy Conversion Principles III Introduction to Rotating Machines IV Synchronous Machines V Polyphase Induction Machines VI DC Machines VII.Variable – Reluctance Machines and Stepping Motors VIII.Single and Two – Phase Motors IX Speed and Torque Control sites.google.com/site/ncpdhbkhn Synchronous Machines Introduction to Polyphase Synchronous Machines Synchronous – Machine Inductances and Equivalent Circuits Performance Characteristics Effects of Salient Poles Power – Angle Characteristics of Salient – Pole Machines Permanent – Magnet AC Motors sites.google.com/site/ncpdhbkhn Introduction to Polyphase Synchronous Machines (1) Synchronous machine: • An AC machine • Speed under steady – state conditions is proportional to the frequency of the (AC) current in its armature winding (on the stator, & usually a three – phase winding) • The rotor (field winding): – There is a magnetic field created by the DC current on the motor – Rotates at the same speed as the rotating magnetic field produced by the armature winding c a Field winding b N Rotor S a b Stator c Armature winding • The DC power required for excitation is supplied by the excitation system sites.google.com/site/ncpdhbkhn Introduction to Polyphase Synchronous Machines (2) • In older machines, the excitation current is supplied through slipping rings from a DC machine • In modern machines, the excitation is supplied from AC exciters & solid – state rectifiers • In other systems (brushless excitation system), the alternator of the AC exciter is on the rotor, & the current is supplied directly to the field winding without any slipping ring sites.google.com/site/ncpdhbkhn Introduction to Polyphase Synchronous Machines (3) A single synchronous generator supplying power to an impedance load: • Acts as a voltage source • Its frequency is determined by the speed of its mechanical drive (the prime mover) • The amplitude of the generated voltage is proportional to the frequency & the field current • The current & power factor are determined by the generator field excitation & the impedance of the generator & the load sites.google.com/site/ncpdhbkhn Introduction to Polyphase Synchronous Machines (4) • • • • Synchronous generators: Can be readily operated in parallel The electricity supply system has hundreds of them operating in parallel, interconnected by thousands of kilometres of transmission lines Must be coordinated both technically & administratively When a synchronous generator is connected to a large interconnected system: – The voltage & frequency at its armature terminals are substantially fixed by the system – Armature currents will produce a component of the air – gap magnetic field which rotates at synchronous speed as determined by the system electrical frequency fe – The fields of the stator & rotor must rotate at the same speed, & therefore the rotor must turn at precisely synchronous speed – It is useful to represent the remainder of the system as a constant – frequency, constant – voltage source, referred to as an “infinte bus” sites.google.com/site/ncpdhbkhn Introduction to Polyphase Magnetic axis Synchronous Machines (5) of rotor poles T R F f sin RF 2 • • • • • a c f b RF ФR: resulting air – gap flux per pole Magnetic axis Ff: mmf of the DC field winding b f c of phase a δRF: electrical phase angle between magnetic axes of ФR & Ff a In a generator: the prime – mover torque acts in the direction of rotation of the rotor, T pushing the rotor mmf wave ahead of the resultant air – gap flux, the g electromechanical torque then opposes rotation Generator o o RF 90 180 In a synchronous motor: the o electromechanical torque is in the direction 90 180o Motor of rotation, in opposition to the retarding torque of the mechanical load on the shaft m sites.google.com/site/ncpdhbkhn Synchronous Machines Introduction to Polyphase Synchronous Machines Synchronous – Machine Inductances & Equivalent Circuits Performance Characteristics Effects of Salient Poles Power – Angle Characteristics of Salient – Pole Machines Permanent – Magnet AC Motors sites.google.com/site/ncpdhbkhn Synchronous – Machines Inductances & Equivalent Circuits (1) Magnetic axis of rotor va ia a aaia abib acic af i f b baia bbib bcic bf i f c caia cbib ccic cf i f a c b f f b f faia fbib fcic ff i f ia m t 0 Magnetic axis c of phase a a va sites.google.com/site/ncpdhbkhn 10 Effect of Salient Poles (2) Fundamental field flux Actual field flux Fundamental armature flux Fundamental field flux Actual field flux Actual armature flux Armature surface Armature surface Pole Third harmonic armature flux Fundamental armature flux Actual armature flux sites.google.com/site/ncpdhbkhn 48 Effect of Salient Poles (3) Axis of field pole Fundamental armature flux Fundamental field flux Actual field flux Actual armature flux Direct axis Armature surface ˆ f Quadrature axis Eˆ af ˆ ar Iˆa Third harmonic armature flux sites.google.com/site/ncpdhbkhn 49 Effect of Salient Poles (4) ˆ ar ˆ ad Iˆq ˆ aq ˆ R Eˆ af Quadrature axis Iˆd Iˆa ˆ f Direct axis sites.google.com/site/ncpdhbkhn 50 Effect of Salient Poles (5) ˆ ˆ Iq Eaf Iˆd jX q Iˆq Vˆa Iˆa jX d Iˆd Ra Iˆa A Iˆd B Iˆa Vˆa D C Xq: Quadrature – axis synchronous reactance Eˆ af G F Xd: Direct – axis synchronous reactance Eˆ af Vˆa Ra Iˆa jX d Iˆd jX q Iˆq Direct axis Iˆq Quadrature axis DE jX q Iˆd EF jX q Iˆq E Ra Iˆa DF DE EF jX q ( Iˆd Iˆq ) jX q Iˆa AF Vˆa Ra Iˆa jX q Iˆa The sum (Vˆa Ra Iˆa jX q Iˆa ) locates the angular position of the generated voltage Eˆ af sites.google.com/site/ncpdhbkhn 51 Effect of Salient Poles (6) Ex Given a salient – pole synchronous generator, its reactances Xd & Xq are 1.00 & 0.60 per unit, respectively, Rarmature ≈ 0, power factor is 0.85 lagging Compute the generated voltage? The sum (Vˆa Ra Iˆa jX q Iˆa ) locates the angular position of the generated voltage Eˆ af cos1 (0.85) 31.8o o 1.00 j 0.60 1.00e j 31.8 1.41e Iˆd B Vˆa A AF Vˆa jX q Iˆa j 21.2o F Iˆq Iˆa 1.00e j 31.8 o Iˆa Eˆ af G D C E Ra Iˆa 21.2o I d I a sin(21.2o 31.8o ) 1.00sin 53o 0.80 I q I a cos(21.2o 31.8o ) 1.00cos53o 0.60 sites.google.com/site/ncpdhbkhn 52 Effect of Salient Poles (7) Ex Given a salient – pole synchronous generator, its reactances Xd & Xq are 1.00 & 0.60 per unit, respectively, Rarmature ≈ 0, power factor is 0.85 lagging Compute the generated voltage? ˆI 1.00e j 31.8o ; I 0.80; I 0.60; 21.2o ; 31.8o a d q Iˆq Eˆ af Vˆa Ra Iˆa jX d Iˆd jX q Iˆq Iˆd o Iˆq 0.60e j 21.2 Direct axis Eˆ af Vˆa Iˆa Ra Iˆa Quadrature ˆ axis jX q I q jX d Iˆd ˆI 0.80e j ( 90o 21.2o ) 0.80e j 68.6o d o o o Eˆ af j1 0.80e j 68.6 j 0.60 0.60e j 21.2 1.73e j 21.2 sites.google.com/site/ncpdhbkhn 53 Effect of Salient Poles (8) Ex Given a salient – pole synchronous generator, its reactances Xd = Xq = Xs = 1.00, Rarmature ≈ 0, power factor is 0.85 lagging Compute the generated voltage? o Iˆa 1.00e j 31.8 Eˆ af Vˆa jX s Iˆa j1 1e j 31.8o 1.75e j 29.1o sites.google.com/site/ncpdhbkhn 54 Synchronous Machines Introduction to Polyphase Synchronous Machines Synchronous – Machine Inductances and Equivalent Circuits Performance Characteristics Effects of Salient Poles Power – Angle Characteristics of Salient – Pole Machines Permanent – Magnet AC Motors sites.google.com/site/ncpdhbkhn 55 Power – Angle Characteristics of Salient – Pole Machines (1) Eˆ af X dT X d X eq SM X eq Xd , Xq X qT X q X eq Iˆq Vd Veq sin Vq Veq cos Iˆd P Vd I d Vq I q Direct axis Eˆ af Vˆeq Veq I d sin Veq I q cos jX eq Iˆa jX eq Iˆq jX d Iˆd jX eq Iˆd Eaf Veq cos X eq I d X d I d Veq cos X dT I d Id Veq sin X eq I q X q I q X qT I q Iq sites.google.com/site/ncpdhbkhn Quadrature axis jX q Iˆq Vˆa Iˆa Vˆeq Eaf Veq cos X dT Veq sin X qT 56 Power – Angle Characteristics of Salient – Pole Machines (2) Eˆ af Xd , Xq P Veq I d sin Veq I q cos Id Iq Eaf Veq cos X dT SM P Eaf Veq X dT sin X eq Veq2 ( X dT X qT ) X dT X qT Vˆeq sin 2 Veq sin X qT sites.google.com/site/ncpdhbkhn 57 Power – Angle Characteristics of Salient – Pole Machines (3) P Eaf Veq X dT sin Veq2 ( X dT X qT ) X dT X qT sin 2 0.6 0.4 P 0.2 -0.2 -0.4 -0.6 -3 -2 -1 (rad) sites.google.com/site/ncpdhbkhn 58 Power – Angle Characteristics of Salient – Pole Machines (4) P • • Eaf Veq Eaf Veq X dT sin Veq2 ( X dT X qT ) X dT X qT sin 2 sin : for a cylindrical – rotor machine X dT Veq2 ( X dT X qT ) X dT X qT sin 2 : – Includes the effect of salient poles – If XdT = XqT (uniform – air – gap machine), then it is zero • The characteristic for negative values of δ is the same except for a reversal in the sign of P – For a generator: δ > – For a motor: δ < sites.google.com/site/ncpdhbkhn 59 Power – Angle Characteristics of Salient – Pole Machines (5) P Eaf Veq X dT sin Veq2 ( X dT X qT ) X dT X qT sin 2 Generator (δ > 0): Veq2 ( X dT X qT ) dP Eaf Veq cos cos 2 max d X dT X dT X qT Pmax P max Motor (δ < 0): Eaf Veq Veq2 ( X dT X qT ) dP cos cos 2 max X dT X qT d X dT Pmax P max sites.google.com/site/ncpdhbkhn 60 Synchronous Machines Introduction to Polyphase Synchronous Machines Synchronous – Machine Inductances and Equivalent Circuits Performance Characteristics Effects of Salient Poles Power – Angle Characteristics of Salient – Pole Machines Permanent – Magnet AC Motors sites.google.com/site/ncpdhbkhn 61 Permanent – Magnet AC Motors • Polyphase synchronous motors with permanent – magnet rotors • Similar to the synchronous machines discussed up to this point, with the exception that the field windings are replaced by permanent magnets can be analysed with the techniques of this chapter by assuming that the machine is excited by a field current of constant value • Frequently referred to as “brushless motors” Rotor magnetic axis a c b sites.google.com/site/ncpdhbkhn N S a b c m t Phase a magnetic axis Permanent – magnet rotor 62 ... Materials II Electromechanical Energy Conversion Principles III Introduction to Rotating Machines IV Synchronous Machines V Polyphase Induction Machines VI DC Machines VII.Variable – Reluctance Machines. .. Given data taken from the open- and short-circuit characteristics of a three-phase, Yconnected, 220-V synchronous machine: The open – circuit characteristic: line-to-line voltage = 220V; field... cos(et e )i f 3Laa Ls Lal (synchronous inductance) sites.google.com/site/ncpdhbkhn 18 Synchronous Machines Introduction to Polyphase Synchronous Machines Synchronous – Machine Inductances