An Application of Power Electronics ELECTRICAL DRIVES: An Application of Power Electronics

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 T1 conducts  va = Vdc Jika vdc=110 Volt dan duti cycle=0.75. Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 2 kuadran

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Jika vdc=110 Volt dan duti cycle=0.75. Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 4 kuadran va = Vdc when Q1 and Q2 are ON Positive current

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 T1 conducts  va = Vdc Jika vdc=110 Volt dan duti cycle=0.75. Tentukan: (a). Va (avg, dan V(rms) (b). Cara Kerja rangkaian untuk operasi 2 kuadran

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D2 conducts  va = 0 T1 conducts  va = Vdc Va Eb Quadrant 1 The average voltage is made larger than the back emf

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D1 conducts  va = Vdc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter Va T1 + Vdc  D1 ia Q2 Q1 Ia + Va - D2 T2 D1 conducts  va = Vdc T2 conducts  va = 0 Eb Va Quadrant 2 The average voltage is made smallerr than the back emf, thus forcing the current to flow in the reverse direction

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter 2vtri vc + vA - Vdc + vc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current va = Vdc when Q1 and Q2 are ON

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current va = Vdc when Q1 and Q2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current Negative current va = Vdc when Q1 and Q2 are ON va = Vdc when D1 and D2 are ON va = -Vdc when D3 and D4 are ON va = 0 when current freewheels through Q and D

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter leg A leg B + Vdc  D1 D3 Q1 Q3 + Va  D4 D2 Q4 Q2 Positive current Negative current va = Vdc when Q1 and Q2 are ON va = Vdc when D1 and D2 are ON va = -Vdc when D3 and D4 are ON va = -Vdc when Q3 and Q4 are ON va = 0 when current freewheels through Q and D va = 0 when current freewheels through Q and D

Power Electronic Converters in ED Systems DC DRIVES Bipolar switching scheme – output swings between VDC and -VDC AC-DC-DC vc + _ Vdc vA - vB 2vtri vc vA Vdc Vdc vB vAB Vdc -Vdc

Power Electronic Converters in ED Systems DC DRIVES Unipolar switching scheme – output swings between Vdc and -Vdc AC-DC-DC Vtri vc -vc Vdc + vA - + vB - vA Vdc vB Vdc vc + vAB Vdc _ -vc

Power Electronic Converters in ED Systems DC DRIVES AC-DC-DC DC-DC: Four-quadrant Converter Armature current Vdc Vdc Armature current Vdc Bipolar switching scheme Unipolar switching scheme Current ripple in unipolar is smaller Output frequency in unipolar is effectively doubled

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Switching signals obtained by comparing control signal with triangular wave Vdc + Va − vtri q vc We want to establish a relation between vc and Va AVERAGE voltage Va(s) vc(s) DC motor ?

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Ttri ton 1 Vc > Vtri Vc < Vtri vc Vdc

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d 0.5 vc -Vtri Vtri -Vtri vc For vc = -Vtri  d = 0

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d -Vtri 0.5 vc -Vtri Vtri vc For vc = -Vtri  d = 0 For vc = 0  d = 0.5 For vc = Vtri  d = 1

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters d -Vtri 0.5 vc -Vtri Vtri vc For vc = -Vtri  d = 0 For vc = 0  d = 0.5 For vc = Vtri  d = 1

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Thus relation between vc and Va is obtained as: Introducing perturbation in vc and Va and separating DC and AC components: DC: AC:

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Taking Laplace Transform on the AC, the transfer function is obtained as: va(s) vc(s) DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme vc vtri + Vdc − q -Vdc + VAB  2vtri vc vA Vdc vB Vdc vAB Vdc -Vdc

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Bipolar switching scheme va(s) vc(s) DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters + Vdc − vc vtri qa -vc qb Leg a Leg b Unipolar switching scheme Vtri vc -vc vA vB vAB The same average value we’ve seen for bipolar !

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Unipolar switching scheme vc(s) va(s) DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Te = kt ia ee = kt  Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m ac components dc components

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet Perform Laplace Transformation on ac components Vt(s) = Ia(s)Ra + LasIa + Ea(s) Te(s) = kEIa(s) Ea(s) = kE(s) Te(s) = TL(s) + B(s) + sJ(s)

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters DC motor – separately excited or permanent magnet + -

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Tc vtri + Vdc − q – kt Torque controller + - Torque controller Converter DC motor

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Design procedure in cascade control structure Inner loop (current or torque loop) the fastest – largest bandwidth The outer most loop (position loop) the slowest – smallest bandwidth Design starts from torque loop proceed towards outer loops

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example OBJECTIVES: Fast response – large bandwidth Minimum overshoot good phase margin (>65o) Zero steady state error – very large DC gain BODE PLOTS Obtain linear small signal model METHOD Design controllers based on linear small signal model Perform large signal simulation for controllers verification

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Closed-loop speed control – an example Ra = 2  La = 5.2 mH J = 152 x 10–6 kg.m2 B = 1 x10–4 kg.m2/sec kt = 0.1 Nm/A ke = 0.1 V/(rad/s) Vd = 60 V Vtri = 5 V fs = 33 kHz PI controllers Switching signals from comparison of vc and triangular waveform

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Torque controller design Open-loop gain kpT= 90 kiT= 18000 compensated compensated

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design Torque loop 1 Speed controller * T* T  – +

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Speed controller design Open-loop gain kps= 0.2 kis= 0.14 compensated compensated

Modeling and Control of Electrical Drives Modeling of the Power Converters: DC drives with SM Converters Large Signal Simulation results Speed Torque

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