ECE 8830 - Electric Drives

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ECE 8830 - Electric Drives
Topic 6 Voltage-Fed Converters
Spring 2004
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Introduction

• Voltage-fed converters convert dc input to ac
  output. These converters can operate
  bidirectionally as either an inverter or as a
  rectifier.
• The input voltage should be stiff -
  indicating that the Thevenin impedance should be
  close to zero. Often the term Voltage Stiff
  Inverters (VSI) is used to describe these types
  of converters.

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Introduction (contd)

• Input Sources
• Utility line or ac generator through
• rectifier/filter.
• Battery, fuel cell, PV array
• Output Format
• Single phase/Polyphase
• Square wave, sine wave, PWM wave,
• stepped wave, or quasi-square wave.

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Single-Phase Inverters

• Half-Bridge Inverter
• One of the simplest types of inverter.
  Produces a square wave output.

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Single-Phase Inverters (contd)

• Full Bridge (H-bridge) Inverter
• Two half-bridge inverters combined.
• Allows for four quadrant operation.

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Single-Phase Inverters (contd)

• Quadrant 1 Positive step-down converter
• (forward motoring)
• Q1-On Q2 - Chopping D3,Q1 freewheeling

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Single-Phase Inverters (contd)

• Quadrant 2 Positive step-up converter
• (forward regeneration)
• Q4 - Chopping D2,D1 freewheeling

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Single-Phase Inverters (contd)

• Quadrant 3 Negative step-down converter
• (reverse motoring)
• Q3-On Q4 - Chopping D1,Q3 freewheeling

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Single-Phase Inverters (contd)

• Quadrant 4 Negative step-up converter
• (reverse regeneration)
• Q2 - Chopping D3,D4 freewheeling

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Single-Phase Inverters (contd)

• Phase-Shift Voltage Control - the output of
  the H-bridge inverter can be controlled by phase
  shifting the control of the component
  half-bridges. See waveforms on next slide.

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Single-Phase Inverters (contd)
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Single-Phase Inverters (contd)

• The waveform of the output voltage vab is a
  quasi-square wave of pulse width ?. The Fourier
  series of vab is given by
• The value of the fundamental, a1
• The harmonic components as a function of phase
  angle are shown in the next slide.

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Single-Phase Inverters (contd)

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Three-Phase Bridge Inverters

• Three-phase bridge inverters are widely used
  for ac motor drives. Two modes of operation -
  square wave and six-step. The topology is
  basically three half-bridge inverters, each
  phase-shifted by 2?/3, driving each of the phase
  windings.

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Three-Phase Bridge Inverters (contd)

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Three-Phase Bridge Inverters (contd)

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Three-Phase Bridge Inverters (contd)

• The three square-wave phase voltages can be
  expressed in terms of the dc supply voltage, Vd,
  by Fourier series as

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Three-Phase Bridge Inverters (contd)

• The line voltages can then be expressed as

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Three-Phase Bridge Inverters (contd)

• The line voltages are six-step waveforms and
  have characteristic harmonics of 6n?1, where n is
  an integer. This type of inverter is referred to
  as a six-step inverter.
• The three-phase fundamental and harmonics are
  balanced with a mutual phase shift of 2?/3.

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Three-Phase Bridge Inverters (contd)

• If the three-phase load neutral n is isolated
  from the the center tap of the dc voltage supply
  (as is normally the case in an ac machine) the
  equivalent circuit is shown below.

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Three-Phase Bridge Inverters (contd)

• In this case the isolated neutral-phase
  voltages are also six-step waveforms with the
  fundamental component phase-shifted by ?/6 from
  that of the respective line voltage. Also, in
  this case, the triplen harmonics are suppressed.

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Three-Phase Bridge Inverters (contd)

• For a linear and balanced 3? load, the line
  currents are also balanced. The individual line
  current components can be obtained from the
  Fourier series of the line voltage. The total
  current can be obtained by addition of the
  individual currents. A typical line current wave
  with inductive load is shown below.

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Three-Phase Bridge Inverters (contd)

• The inverter can operate in the usual
  inverting or motoring mode. If the phase current
  wave, ia, is assumed to be perfectly filtered and
  lags the phase voltage by ?/3 the voltage and
  current waveforms are as shown below

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Three-Phase Bridge Inverters (contd)

• The inverter can also operate in rectification
  or regeneration mode in which power is pushed
  back to the dc side from the ac side. The
  waveforms corresponding to this mode of operation
  with phase angle 2?/3 are shown below

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Three-Phase Bridge Inverters (contd)

• See Bose text for Input Ripple and Device
  Ratings.

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Three-Phase Bridge Inverters (contd)

• The phase-shift voltage control principle
  described earlier for the single-phase inverter
  can be extended to control the output voltage of
  a three-phase inverter.

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Three-Phase Bridge Inverters (contd)

• The circuit shows three H-bridge inverters
  (one for each phase winding) where each H-bridge
  is connected to the primary winding of a
  transformer. The output voltages are derived from
  the transformers secondary windings connected in
  a wye configuration.

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Three-Phase Bridge Inverters (contd)

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Three-Phase Bridge Inverters (contd)

• The three waveforms va0,vb0, and vc0 are of
  amplitude 0.5Vd and are mutually phase-shifted by
  2?/3.
• The three waveforms ve0,vf0, and vg0 are of
  similar but phase shifted by ?.

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Three-Phase Bridge Inverters (contd)

• The transformers secondary phase voltages,
  vA0, vB0, and vc0 may be expressed as follows
• where m is the transformer turns ratio
• ( Ns/Np). Note that each of these waves is a
  function of ? angle.

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Three-Phase Bridge Inverters (contd)

• The output line voltages are given by
• While the component voltage waves va0, vd0, vA0
  etc. all contain triplen harmonics, they are
  eliminated from the line voltages because they
  are co-phasal. Thus the line voltages are
  six-step waveforms with order of harmonics 6n?1
  at a phase angle ?.

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Three-Phase Bridge Inverters (contd)

• The Fourier series for vA0 and vB0 are given
  by

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Three-Phase Bridge Inverters (contd)

• The Fourier series for vAB is given by
• Note that the triplen harmonics are removed in
  vAB although they are present in vA0 and vB0.

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Three-Phase Bridge Inverters (contd)

• See text for a description of Voltage and
  Frequency Control for the three-phase H-bridge
  inverter.

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Three-Phase Bridge Inverters (contd)

• A twelve-step inverter can be created by
  combining two six-step inverters.

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Three-Phase Bridge Inverters (contd)

• Features of the 12-step inverter
• The lower bridge is phase shifted by ?/6 with
  respect to the upper bridge.
• Each inverter is connected to the primary delta
  winding of each transformer.
• Upper bridge transformer only has one secondary
  winding per phase whereas lower bridge
  transformer has two secondary windings per phase.
  
• Note the difference in turns ratio for the two
  transformers.

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Three-Phase Bridge Inverters (contd)

• Phasor diagram for voltage synthesis and
  output voltage waveform are shown below

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Three-Phase Bridge Inverters (contd)

• The output phase voltages are obtained by the
  interconnection of three secondary windings to
  satisfy the phasor diagram on the previous slide,
  e.g. vNA vabvde-vef

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Three-Phase Bridge Inverters (contd)

• Since the lower bridge lags by ?/6,
  considering vab as the reference, the Fourier
  series of the component voltages are given by
• where n is the turns ratio of the upper
  transformer.

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Three-Phase Bridge Inverters (contd)

• The fundamental component of vNA is given by
• The output phase voltage Fourier series can be
  expressed as
• Note the lower harmonic content compared to
  the six-step inverter.

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Three-Phase Bridge Inverters (contd)

• See Bose text for 18-step inverter.

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Simulating Three-Phase Bridge Inverters

• The below figure shows a SIMULINK block diagram
  for a 3-phase voltage-fed inverter.