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**An Application of Power Electronics**

ELECTRICAL DRIVES: An Application of Power Electronics

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**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

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**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

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**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

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**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

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**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

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**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

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**Power Electronic Converters in ED Systems**

DC DRIVES AC-DC-DC DC-DC: Two-quadrant Converter 2vtri vc + vA - Vdc + vc

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**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

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**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 = when current freewheels through Q and D

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**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 = when current freewheels through Q and D

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**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 = when current freewheels through Q and D va = when current freewheels through Q and D

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**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

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**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

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**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

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**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 ?

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**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

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**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

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**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

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**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

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**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:

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**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

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**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

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**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

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**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 !

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**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

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**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

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**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)

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**Modeling and Control of Electrical Drives**

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

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**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

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**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

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**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

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**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

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**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

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**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 – +

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**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

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**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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