This chapter include all of the following content: Elementary concepts, introduction to AC and DC machines, MMF of distributed windings, magnetic fields in Rotating machinery, rotating MMF Waves in AC machines, generated voltage,...
Nguyễn Công Phương ELECTROMECHANICAL ENERGY CONVERSION Introduction to Rotating 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 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines MMF of Distributed Windings Magnetic Fields in Rotating Machinery Rotating MMF Waves in AC Machines Generated Voltage Torque in Nonsalient – Pole Machines Linear Machines Magnetic Saturation 10.Leakage Fluxes sites.google.com/site/ncpdhbkhn Elementary Concepts (1) • In rotating machines, voltage are generated in windings or groups of coils by rotating these windings mechanically through a magnetic field: – By mechanically rotating a magnetic field past the winding, or – By designing the magnetic circuit so that the reluctance varies with rotation of the rotor • A set of such coils connected together is typically referred to as an armature winding • In AC machines (e.g synchronous or induction), the armature winding is typically on the stationary – portion of the motor (referred to as the stator) • In DC machines, the armature winding is on the rotating portion of the motor (referred to as the rotor) sites.google.com/site/ncpdhbkhn Elementary Concepts (2) • Second winding(s) carrying DC currents and used to produce the main operating flux in the machine is called field winding – For a DC machine, it is on the stator – For a synchonous machine, it is on the rotor – Sometimes it is a permanent magnet • The time – varying flux tends to induce currents, known as eddy currents, in the electrical steel • There are no windings on the rotor of some machines, such as variable reluctance machines and stepper motors sites.google.com/site/ncpdhbkhn Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines a) AC Machines i ii b) 10 Synchronous Machines Induction Machines DC Machines MMF of Distributed Windings Magnetic Fields in Rotating Machinery Rotating MMF Waves in AC Machines Generated Voltage Torque in Nonsalient – Pole Machines Linear Machines Magnetic Saturation Leakage Fluxes sites.google.com/site/ncpdhbkhn Synchronous Machines (1) • A simple, two – pole, single – phase synchronous generator • The field – winding, producing a single pair of magnetic poles, is excited by direct current conducted to it by means of stationary carbon brushes which contact rotating slip rings or collector rings • The single, low – power field winding on the rotor; the high – power, typically multiple – phase, armature winding on the stator Armature – winding magnetic axis θa Field winding −a a Rotor N – turn armature winding sites.google.com/site/ncpdhbkhn Stator Flux paths Synchronous Machines (2) • The two coil sides (of the armature winding) a & –a placed in diametrically opposite narrow slots on the inner periphery of the stator • The conductors forming the coil sides are parallel to the shaft of the machine • The rotor is turned at a constant speed by a source of mechanical power connected to the shaft Armature – winding magnetic axis θa Field winding −a a Rotor N – turn armature winding sites.google.com/site/ncpdhbkhn Stator Flux paths Synchronous Machines (3) • The flux – linkages of the armature winding change with time • If the flux distribution is sinusoidal & the rotor speed is constant, then the resulting coil voltage will be sinusoidal in time • The frequency (Hz, cycles per second) of the coil voltage is the same as the speed of the rotor (revolutions per second) • The electric frequency of the generated voltage is synchronized with the mechanical speed the name “synchronous” • 3000 rpm 50 Hz sites.google.com/site/ncpdhbkhn Armature – winding magnetic axis θa −a a Stator Synchronous Machines (4) − a1 θ ae = poles θa poles n fe = × 60 a1 a2 B 0.8 0.6 0.4 −a1 a1 −a a2 2π π 0.2 4π 2π -0.2 θ a , mechanical radians −a θ ae, electrical radians -0.4 -0.6 -0.8 -1 10 12 sites.google.com/site/ncpdhbkhn 10 Magnetic Field Viewpoint (2) Fr H ag g = Fsr (δ sr ) δ sr Fs Fsr = F + F + Fs Fr cos δ sr s (H ) ag peak r Stator Fsr = g Fr Coenergy density of the air-gap : Average coenergy density : µ0 Fr sin δ sr H ag = Fsr sin δ s δs Fs sin δ sr µ0 ( H ) = Fsr sin δ r → Average coenergy density : δ sr Fs ag peak δr Fsr µ0 Fsr g sites.google.com/site/ncpdhbkhn 64 Magnetic Field Viewpoint (3) Average coenergy density : µ0 Fsr Fr δ sr g ′ = (average coenergy density) × (volume of air gap) W fld Fs Stator µ F 2 µ0π Dl sr = Fsr × (π Dlg ) = 4g g Fsr = Fs2 + Fr2 + Fs Fr cos δ sr ′ = → W fld Ttwo− pole = Tmultipole µ0π Dl 4g ( Fs2 + Fr2 + Fs Fr cos δ sr ) ′ ∂W fld ∂δ sr =− Fs , Fr are const µ0π Dl 2g Fs Fr sin δ sr poles µ0π Dl = − Fs Fr sin δ sr 2g sites.google.com/site/ncpdhbkhn 65 Magnetic Field Viewpoint (4) Tmultipole Fr δ sr poles µ0π Dl = − Fs Fr sin δ sr 2g Fs Stator • • • • • • • δsr is the electrical space – phase angle between the rotor & stator mmf waves The torque T acts in the direction to accelerate the rotor When δsr is positive, the torque is negative & the machine is operating as a generator When δsr is negative, the torque is positive & the machine is operating as a motor The torque is proportional to the peak values of the stator– & rotor–mmf waves Fs & Fr, and to the sine of the electrical space – phase angle δsr between them Minus sign: the fields tend to align themselves Equal & opposite torques are exerted on the stator & rotor sites.google.com/site/ncpdhbkhn 66 Magnetic Field Viewpoint (5) Tmultipole Fr poles µ0π Dl = − Fs Fr sin δ sr 2g Tmultipole = − δ sr Fs poles Lsr isir sin θ me poles µ0π Dl T = − Fs Fsr sin δ s 2g poles µ0π Dl = − Fr Fsr sin δ r 2g Stator Fr Fr sin δ sr = Fsr sin δ s Fsr µ0 Fsr gBsr H sr = → Bsr = → Fsr = g g µ0 δr Fsr δ sr δs Fs Fs sin δ sr = Fsr sin δ r poles π Dl →T = − Bsr Fr sin δ r sites.google.com/site/ncpdhbkhn 67 Magnetic Field Viewpoint (6) Ex A 2400 r/min, four – pole, 50 Hz synchronous motor has an air – gap length of 1mm The average diameter of the air – gap is 27 cm, & its axial length is 32 cm The rotor winding has 800 turns & a winding factor of 0.976 The maximum rotor current is 18A, the maximum Bsr = 2T, find the maximum torque & power output? Fr = → ( Fr ) max = kr N r I r poles cos θr π poles k r N r ( I r ) max 0.976 × 800 × 18 = = 4474A π poles π poles π Dl T = − Bsr Fr sin δ r π × 0.27 × 0.32 poles π Dl → Tmax = B ( F ) = × 4474 = 2429Nm sr r max 2 Pmax = ωmTmax = ns π 30 Tmax = 2400 π 30 2429 = 610kW sites.google.com/site/ncpdhbkhn 68 Magnetic Field Viewpoint (7) Φ p = (average value of B over a pole) × (pole area) 2 π Dl Dl = B peak × = B peak π poles poles poles π Dl T = − Bsr Fr sin δ r =− π poles 2 2 Φ sr Fr sin δ r sites.google.com/site/ncpdhbkhn 69 Torque in Nonsalient – Pole Machines T =− poles Lsris ir sin θ me poles µ0π Dl T = − Fs Fr sin δ sr 2g poles π Dl T = − Bsr Fr sin δ r T =− π poles 2 2 Φ sr Fr sin δ r The torque is proportional to the product of the magnitudes of the interacting fields, and to the sine of the electrical space angle between their magnetic axes sites.google.com/site/ncpdhbkhn 70 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines MMF of Distributed Windings Magnetic Fields in Rotating Machinery Rotating MMF Waves in AC Machines Generated Voltage Torque in Nonsalient – Pole Machines Linear Machines Magnetic Saturation 10.Leakage Fluxes sites.google.com/site/ncpdhbkhn 71 Linear Machines (1) • The most widely known use of linear motors is in the transportation field: – The moving vehicle: the AC “stator”, and – The rails: the conducting stationary “rotor” • Also in the machine tool industry & in robotics • The analysis of linear machines is quite similar to that of rotating mchines: – Angle – Torque displacement, and force sites.google.com/site/ncpdhbkhn 72 Linear Machines (2) Fag Ni Ni Fag = cos θ a → H ag = = cos θ a g π 2g π 2π z θa = β → H ag = Ni Ni − Fag Ni 2π z cos π 2g β Fundamental Fag1 β /2 z g sites.google.com/site/ncpdhbkhn 73 Linear Machines (3) Ni 2π z H ag = cos π 2g β (concentrated) kw N phi 2π z H ag = cos π pg β (distributed) ia = I m cos ωet o i = I cos( t − 120 ) ω b m e i = I cos(ω t + 120o ) c m e → F + ( z, t ) = 2π z Fmax cos − ωe t β Fmax kw N ph ωe β = Im, v = = fe β π 2p 2π sites.google.com/site/ncpdhbkhn 74 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines MMF of Distributed Windings Magnetic Fields in Rotating Machinery Rotating MMF Waves in AC Machines Generated Voltage Torque in Nonsalient – Pole Machines Linear Machines Magnetic Saturation 10.Leakage Fluxes sites.google.com/site/ncpdhbkhn 75 Magnetic Saturation • Magnetic materials are less than ideal As their magnetic flux is increased, they begin to saturate • Therefore saturation may influence the characteristics of the machines • With saturation, it is more difficult to obtain analytical results • Saturation characteristics of rotating machines are typically presented in the form of an “open – circuit characteristic” or ”magnetization curve” or ”saturation curve” sites.google.com/site/ncpdhbkhn 76 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines MMF of Distributed Windings Magnetic Fields in Rotating Machinery Rotating MMF Waves in AC Machines Generated Voltage Torque in Nonsalient – Pole Machines Linear Machines Magnetic Saturation 10.Leakage Fluxes sites.google.com/site/ncpdhbkhn 77 Leakage Fluxes + + λ2 − λ3 − Coil Coil ϕ13 ϕ12 ϕ123 I1 ϕ1l + λ1 − Coil sites.google.com/site/ncpdhbkhn 78 ... sites.google.com/site/ncpdhbkhn Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines a) AC Machines i ii b) 10 Synchronous Machines Induction Machines DC Machines MMF of Distributed... sites.google.com/site/ncpdhbkhn 14 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines a) AC Machines i ii b) 10 Synchronous Machines Induction Machines DC Machines MMF of Distributed... 26 Introduction to Rotating Machines Elementary Concepts Introduction to AC and DC Machines MMF of Distributed Windings a) AC Machines b) DC Machines Magnetic Fields in Rotating Machinery Rotating