Chapter 10

Chapter 10 - 10-1 Chapter 10 Sinusoidal Permanent Magnet AC...

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Unformatted text preview: 10-1 Chapter 10 Sinusoidal Permanent Magnet AC Drives, Load-Commutated-Inverter Synchronous Motor Drives, and Synchronous Generators Exit 2001 by N. Mohan Print TOC " ! 10-2 Permanent-Magnet AC (PMAC) Drives Power Processing Utility Control input Unit Controller Sinusoidal ia ib ic PMAC Load Position sensor motor θ m (t ) ❏ System level operation similar to DC machines but without brushes - sometimes called Brush-less DC Drives ❏ Motor essentially a synchronous machine whose field flux is provided by permanent magnets Exit 2001 by N. Mohan TOC " ! 10-3 Structure of Permanent-Magnet Synchronous Machines b − axis !!" Br (t ) ib θm N S ia a − axis ic θ m (t ) a − axis c − axis ❏ Permanent Magnet rotor ❏ Sinusoidally distributed stator windings Exit 2001 by N. Mohan TOC " ! 10-4 Principle of Operation ❏ Magnets shaped to produce sinusoidal flux density distribution b − axis !" is !! " ˆ Br (t ) = Br ∠θ m (t ) θ is (t ) = θ m (t ) + 900 • δ = 90o maximizes torque/ampere • Stator current space vector is controlled so that it leads the peak rotor flux by 90 degrees Exit 2001 by N. Mohan a' θm δ = 90oN ❏ Controlled stator currents " • is (t ) controlled by PPU (controlling ia (t ), ib (t ), and ic (t ) ) such that " ˆ is (t ) = I s (t ) ∠θ is (t ), where ib !!" Br ia a − axis S ic a c − axis ˆ Is !" is !!" Br θm N a − axis S TOC " ! 10-5 Torque Calculation !" is dξ f em = Bli Using ξ S dTem (ξ ) = r ˆ Br cos ξ $&% % ' ˆ Is Ns ˆ cos ξ ⋅ dξ ⋅ # ⋅ Is ⋅ $ &% % ' 2% $%&%% ' flux density at ξ cond .length !!" Br N diff no. of cond . at ξ ξ =π / 2 Tem Ns ˆ ˆ π / 2 N ˆ ˆ r #Br I s ∫ cos 2 ξ ⋅ dξ = π s r #Br I s = 2 × ∫ dTem (ξ ) = 2 2 2 ξ =−π / 2 −π / 2 N ˆ ˆ ⇒ Tem = k I s , where the machine torque constant, kT = π s r # Br 2 T ˆ ❏ Torque is proportional to I s alone, just as in dc motors with constant field excitation. Hence the name Brush-Less DC Exit 2001 by N. Mohan TOC " ! Similarity Between DC Motor and Brushless DC Motor ωm φf N S (stationary) S 10-6 !" is δ = 90 o N ωm !!" Br φa (stationary) Brush-Less DC motor drive !!" • Br produced by rotor magnets • Stationary φ f produced and rotates with the rotor by stator windings !" • φa produced by rotating rotor • is produced by stator winding currents and is made to rotate windings and is made at rotor speed by the action of stationary by commutator the PPU action Exit TOC " ! 2001 by N. Mohan DC motor 10-7 Mechanical System Tem Motor Load TL dω m Tem − TL αm = = dt J eq t ω m (t ) = ω m (0 ) + ∫o α m (τ ) ⋅ dτ t θ m (t ) = θ m (0 ) + ∫o ω m (τ ) ⋅ dτ Exit 2001 by N. Mohan TOC " ! 10-8 Calculation of the Reference * * * Values: ia , ib and ic ❏ Reference values are generated by the controller based on desired torque output and rotor position ❏ Reference values tell the PPU what stator currents to deliver ❏ Starting with the desired torque and known rotor position, the desired stator currents are found as follows: * (Tem ,θ m ) * T (t ) ˆ* I s (t ) = em kT θ i* (t ) = θ m (t ) + 900 s " ˆ* is* (t ) = I s (t )∠θ i* (t ) s Exit 2001 by N. Mohan ! " * * * → (is ) → (ia , ib , ic ) " 2 2 ˆ* * ia (t ) = Re is* (t ) = I s (t )cosθ i* (t ) s 3 3 2 "* 2 ˆ* * ib (t ) = Re is (t )∠ − 1200 = I s (t )cos(θ i* (t ) − 1200 ) s 3 3 " 2 2 ˆ* * ic (t ) = Re is* (t )∠ − 2400 = I s (t )cos(θ i* (t ) − 2400 ) s 3 3 TOC " ! 10-9 Example kT = 0.5 Nm/A To produce a counter clockwise holding torque of 5 Nm at θ m = 45° !!" Br b − axis ib !" is 135 o ˆ T I s = em = 10 A kT 45o N ia θ is = θ m + 900 = 1350 a − axis S ic " ˆ is = I s ∠θ is = 10∠1350 c − axis ia = 2ˆ I s cosθ is = −4.71 A 3 ic = 2ˆ I s cos(θ is − 2400 ) = −1.73 A 3 ib = 2ˆ I s cos(θ is − 1200 ) = 6.44 A 3 Stator currents are dc in this example. Exit 2001 by N. Mohan TOC " ! 10-10 Induced EMF in Stator Windings under Balanced Sinusoidal Steady State !!" 1. Br (t ) rotates with an instantaneous speed of ω m (t ) . This rotating flux-density distribution cuts the stator windings to induce a back-emf. !" 2. The rotating flux-density distribution due to rotating is (t ) space vector induces an emf in the stator windings. Exit 2001 by N. Mohan TOC " ! 10-11 Induced EMF in the!! !!! Stator Windings due " " to Rotating Br (ems ,!!" ) B r !!! " " 3 N s !!!! ems (t ) = jω ( π r # ) Bms (t ) (Eq. 9-41) 2 2 with substitutions in the current case: !!! " !!" !! (t ) = jω ( 3 π r # N s ) B (t ) " ems , B m r r 2 2 Voltage Constant: ωm t =0 !!!!!!! " ems, !!" B a − axis r N ωm N ˆ V Nm = kT = π r # s Br kE 2 rad / s A !!! " !! (t ) = j 3 k ω ∠θ (t ) = 3 k ω ∠(θ (t ) + 90 o ) ems , B" E m m E m m r 2 2 Exit 2001 by N. Mohan TOC " ! 10-12 Induced EMF in the Stator Windings due ! !!! " " to Rotating is (ems ,i!" ) s !!! " !!! " ems (t ) = jω Lm ims (t ) (Eq. 9-40) !!!!!! " ems, i!" ωm t =0 s !" is with substitutions in the current case: !! " !" ! (t ) = jω L i (t ) " es ,i m m s s ˆ = ω m Lm I s ∠(θ m (t ) + 90 o + 90 o ) $%&%' θ is (t ) a − axis N !!" Br ωm Lm : Magnetizing inductance Exit 2001 by N. Mohan TOC " ! 10-13 Net induced EMF in the stator windings !!! " ems (t ) ωm t =0 ( !!!" ems ) !!!!!! " ems, i!" s !" is !!!!!!! a − axis " ems, !!" B r Ema Ema, i!" s !!" Ema, B N r !!" Br ωm Space vector diagram Ia ref − axis Phasor diagram for phase-a !!! " !!! " !!! " !!" (t ) + e , !" (t ) ems (t ) = ems , B ms i r s !!! " ! " 3 o ems (t ) = k Eω m ∠(θ m (t ) + 90 ) + jω m Lm is (t ) 2 2 Ema = k Eω m ∠(θ m (t ) + 90 o ) + j ω m Lm I a 3 Exit 2001 by N. Mohan TOC " ! 10-14 Per-Phase Equivalent Circuit L Ia I a ( jω m Ls ) Va + I a Rs Rs (%%%% s )%%%% * Lls Lm + + Ema, i!" − s Va r Ia − !!" Ema, B Ema, i!" − !!" Ema, B + r s − ref − axis ˆ " = 2 E " =k E ω m = E fa ˆ ˆ Ea ,B ms ,Br r 3 Ls = L#s + Lm Lm : Magnetizing inductance Lls : Stator leakage inductance Va = E fa + jω m Ls I a + Rs I a Rs can often be ignored Exit 2001 by N. Mohan TOC " ! 10-15 Controller and Power Processing Unit Power Processing Utility Control input Unit Controller Sinusoidal ia ib ic PMAC Load Position sensor motor θ m (t ) ❏ Controller determines desired phase currents based on desired torque and motor position Exit 2001 by N. Mohan TOC " ! 10-16 Hysterisis current control actual current reference current t 0 * Tem + phase a Vd − 1 kT * ia (t ) ˆ* Is * ib (t ) * ic (t ) + Σ − ia (t ) q A (t ) θ m (t ) Exit 2001 by N. Mohan TOC " ! 10-17 Load-Commutated-Inverter (LCI) Supplied Synchronous Motor Drives Id If Ld ac line input Line-commutated converter Load-commutated inverter Synchronous motor ❏ High power levels ❏ Field windings on rotor carrying a dc current ❏ Thyristor PPU needed at these power levels ❏ DC-link between utility and inverter is a nearly constant current ( I d ) rather than a constant voltage ( Vd ) as in previous circuits ❏ Inverter thyristors commutated by load (synchronous motor) Exit 2001 by N. Mohan TOC " ! 10-18 Synchronous Generators ❏ Generally larger sizes ❏ Directly connected to utility without PPU ❏ Three-phase winding on stator - DC field winding on rotor ❏ Angle between rotor flux and stator flux not necessarily 90o allowing generator to sink or source VARS Exit 2001 by N. Mohan TOC " ! 10-19 Per-Phase Model and Power-Angle Characteristics Pem steady state stability limit Ia + ˆ E fa = E f ∠δ jX s − generator mode + ˆ Va = Va ∠0 o −90 o 90 o δ − motoring mode ❏ Total 3-phase power ˆ ˆ 3 Ef V Pem = sin δ 2 Xs 0 steady state stability limit ❏ For angles between -90o and +90o rotor speed remains locked to line frequency ❏ When the machine is asked to either supply or absorb to much power the angle will move outside the ±90 o range. In this situation the rotor will no longer be synchronized to the line and will either speed up out of control or slow down. In either case excessive currents should trip the circuit breakers. Exit 2001 by N. Mohan TOC " ! 10-20 Adjusting Reactive Power and Power Factor E fa E fa E fa jX s I a 90 o jX s I a δ Ia Va I a ,q δ Va I a ,q { δ jX s I a Ia Va Ia 90 o ❏ Unity Power Factor Operation For every operating condition there is one value of field current that will cause the generator to deliver only real power. ❏ Over-excitation Increasing field current causes generator to supply more reactive power. ❏ Under-excitation When field current is decreased below the value for Unity Power Factor operation, the generator will absorb reactive power. Exit 2001 by N. Mohan TOC " ! 10-21 Summary ❏ List various names associated with the PMAC drives and the reasons behind them. ❏ Draw the overall block diagram of a PMAC drive. Why must they operate in a closed-loop? ❏ How do sinusoidal PMAC drives differ from the ECM drives described in Chapter 7? ❏ Ideally, what are the flux-density distributions produced by the rotor and the stator phase windings? ❏ What does the space vector represent? ❏ In PMAC drives, why at all times is the space vector placed 90 degrees ahead of the space vector in the intended direction of rotation? ❏ Why do we need to measure the rotor position in PMAC drives? Exit 2001 by N. Mohan TOC " ! 10-22 Summary ❏ What does the electromagnetic torque produced by a PMAC drive depend on? ❏ How can regenerative braking be accomplished in PMAC drives? ❏ Why are PMAC drives called self-synchronous? How is the frequency of the applied voltages and currents determined? Are they related to the rotational speed of the shaft? ❏ In a p-pole PMAC machine, what is the angle of the space vector in relation to the phase-a axis, for a given ? ❏ What is the frequency of currents and voltages in the stator circuit needed to produce a holding torque in a PMAC drive? ❏ In calculating the voltages induced in the stator windings of a PMAC motor, what are the two components that are superimposed? Describe the procedure and the expressions. Exit 2001 by N. Mohan TOC " ! 10-23 Summary ❏ Does in the per-phase equivalent circuit of a PMAC machine have the same expression as in Chapter 9? Describe the differences, if any. ❏ Draw the per-phase equivalent circuit and describe its various elements in PMAC drives. ❏ Draw the controller block diagram and describe the hysteresis control of PMAC drives. ❏ What is an LCI-synchronous motor drive? Describe it briefly. ❏ For what purpose are line-connected synchronous generators used? ❏ Why are there problems of stability and loss of synchronism associated with line-connected synchronous machines? ❏ How can the power factor associated with synchronous generators be made to be leading or lagging? Exit 2001 by N. Mohan TOC " ! ...
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