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Ch3slides

# Ch3slides - Chapter 3 Steady-State Equivalent Circuit...

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Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 1 Chapter 3. Steady-State Equivalent Circuit Modeling, Losses, and Efficiency 3.1. The dc transformer model 3.2. Inclusion of inductor copper loss 3.3. Construction of equivalent circuit model 3.4. How to obtain the input port of the model 3.5. Example: inclusion of semiconductor conduction losses in the boost converter model 3.6. Summary of key points

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Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 2 3.1. The dc transformer model Basic equations of an ideal dc-dc converter: P in = P out V g I g = V I ( η = 100%) V = M ( D ) V g (ideal conversion ratio) I g = M ( D ) I These equations are valid in steady-state. During transients, energy storage within filter elements may cause P in P out Switching dc-dc converter D Control input Power input Power output I g I + V + V g
Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 3 Equivalent circuits corresponding to ideal dc-dc converter equations P in = P out V g I g = V I V = M ( D ) V g I g = M ( D ) I Dependent sources DC transformer Power output + V I + M ( D ) V g Power input + V g I g M ( D ) I D Control input Power input Power output + V + V g I g I 1 : M ( D )

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Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 4 The DC transformer model Models basic properties of ideal dc-dc converter: conversion of dc voltages and currents, ideally with 100% efficiency conversion ratio M controllable via duty cycle Solid line denotes ideal transformer model, capable of passing dc voltages and currents Time-invariant model (no switching) which can be solved to find dc components of converter waveforms D Control input Power input Power output + V + V g I g I 1 : M ( D )
Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 5 Example: use of the DC transformer model 1. Original system 2. Insert dc transformer model 3. Push source through transformer 4. Solve circuit V = M ( D ) V 1 R R + M 2 ( D ) R 1 D R V 1 R 1 + + V g + V Switching dc-dc converter 1 : M ( D ) R V 1 R 1 + + V g + V R M ( D ) V 1 M 2 ( D ) R 1 + + V

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Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 6 3.2. Inclusion of inductor copper loss Dc transformer model can be extended, to include converter nonidealities. Example: inductor copper loss (resistance of winding): Insert this inductor model into boost converter circuit: L R L L + C R + v 1 2 i V g R L
Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 7 Analysis of nonideal boost converter switch in position 1 switch in position 2 L + C R + v 1 2 i V g R L L R L + i C R + v + v L i C V g L R L + i C R + v + v L i C V g

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Fundamentals of Power Electronics Chapter 3: Steady-state equivalent circuit modeling, ... 8 Circuit equations, switch in position 1 Inductor current and capacitor voltage: v L ( t ) = V g i ( t ) R L i C ( t ) = – v ( t ) / R Small ripple approximation: v L ( t ) = V g I R L i C ( t ) = – V / R L R L + i C R + v + v L i C V g
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