Ch18 Low Harmonic Modeling and Control

Ch18 Low Harmonic Modeling and Control - Chapter 18 Low...

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ECEN5807 Power Electronics 2 1 Chapter 18: Low harmonic rectifier modeling and control Chapter 18 Low Harmonic Rectifier Modeling and Control 18.1 Modeling losses and efficiency in CCM high-quality rectifiers Expression for controller duty cycle d ( t ) Expression for the dc load current Solution for converter efficiency η Design example 18.2 Controller schemes Average current control Feedforward Current programmed control Hysteretic control Nonlinear carrier control 18.3 Control system modeling Modeling the outer low-bandwidth control system Modeling the inner wide-bandwidth average current controller
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ECEN5807 Power Electronics 2 2 Chapter 18: Low harmonic rectifier modeling and control 18.1 Modeling losses and efficiency in CCM high-quality rectifiers Objective: extend procedure of Chapter 3, to predict the output voltage, duty cycle variations, and efficiency, of PWM CCM low harmonic rectifiers. Approach: Use the models developed in Chapter 3. Integrate over one ac line cycle to determine steady-state waveforms and average power. Boost example + Q 1 L C R + v(t) D 1 v g (t) i g (t) R L i(t) + R + v(t) v g (t) i g (t) R L i(t) DR on + D' : 1 V F Dc-dc boost converter circuit Averaged dc model
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ECEN5807 Power Electronics 2 3 Chapter 18: Low harmonic rectifier modeling and control Modeling the ac-dc boost rectifier R v ac (t) i ac (t) + v g (t) i g (t) + v(t) i d (t) Q 1 L C D 1 controller i(t) R L + R + v(t) = V v g (t) i g (t) R L i(t) = I d(t) R on + d'(t) : 1 V F i d (t) C (large) Boost rectifier circuit Averaged model
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ECEN5807 Power Electronics 2 4 Chapter 18: Low harmonic rectifier modeling and control Boost rectifier waveforms 0 2 4 6 8 10 0 100 200 300 v g (t) v g (t) i g (t) i g (t) 0 ° 30 ° 60 ° 90 ° 120 ° 150 ° 180 ° d(t) 0 0.2 0.4 0.6 0.8 1 0 ° 30 ° 60 ° 90 ° 120 ° 150 ° 180 ° 0 1 2 3 4 5 6 i d (t) i(t) = I ϖ t 0 ° 30 ° 60 ° 90 ° 120 ° 150 ° 180 ° Typical waveforms (low frequency components) i g ( t ) = v g ( t ) R e
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ECEN5807 Power Electronics 2 5 Chapter 18: Low harmonic rectifier modeling and control Example: boost rectifier with MOSFET on-resistance + R + v(t) = V v g (t) i g (t) i(t) = I d(t) R on d'(t) : 1 i d (t) C (large) Averaged model Inductor dynamics are neglected, a good approximation when the ac line variations are slow compared to the converter natural frequencies
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ECEN5807 Power Electronics 2 6 Chapter 18: Low harmonic rectifier modeling and control 18.1.1 Expression for controller duty cycle d(t) + R + v(t) = V v g (t) i g (t) i(t) = I d(t) R on d'(t) : 1 i d (t) C (large) Solve input side of model: i g ( t ) d ( t ) R on = v g ( t ) – d '( t ) v with i g ( t ) = v g ( t ) R e eliminate i g ( t ) : v g ( t ) R e d ( t ) R on = v g ( t ) – d '( t ) v v g ( t ) = V M sin ϖ t solve for d ( t ) : d ( t ) = v v g ( t ) v v g ( t ) R on R e Again, these expressions neglect converter dynamics, and assume that the converter always operates in CCM.
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ECEN5807 Power Electronics 2 7 Chapter 18: Low harmonic rectifier modeling and control 18.1.2 Expression for the dc load current + R + v(t) = V v g (t) i g (t) i(t) = I d(t) R on d'(t) : 1 i d (t) C (large) Solve output side of model, using charge balance on capacitor C : I = i d T ac i d ( t ) = d '( t ) i g ( t ) = d '( t ) v g ( t ) R e But d’ ( t ) is: d '( t ) = v g ( t ) 1 – R on R e v
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