Topic 6: Voltage-Fed Converters

Spring 2004

ECE 8830 - Electric Drives

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.

Introduction (cont’d)

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.

Single-Phase Inverters

Half-Bridge Inverter

One of the simplest types of inverter. Produces a square wave output.

Single-Phase Inverters (cont’d)

Full Bridge (H-bridge) Inverter

Two half-bridge inverters combined. Allows for four quadrant operation.

Single-Phase Inverters (cont’d)

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

Single-Phase Inverters (cont’d)

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

Single-Phase Inverters (cont’d)

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

Single-Phase Inverters (cont’d)

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

Single-Phase Inverters (cont’d)

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.

Single-Phase Inverters (cont’d)

Single-Phase Inverters (cont’d)

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.

1,3,5...

4sin cos

2d

abn

V nv n t

n

4sin / 2dV

Single-Phase Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

Three-Phase Bridge Inverters (cont’d)

Three-Phase Bridge Inverters (cont’d)

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

10

1,3,5...

2( 1) cos( )nd

an

Vv n t

10

1,3,5...

2 2( 1) cos( )

3nd

bn

Vv n t

10

1,3,5...

2 2( 1) cos( )

3nd

cn

Vv n t

Three-Phase Bridge Inverters (cont’d)

The line voltages can then be expressed as:

0 01,3,5...

2 3cos( / 2) cos( 2)d

bc b cn

Vv v v t n t

0 01,3,5...

2 3cos( 5 / 6) cos( 5 6)d

ca c an

Vv v v t n t

0 01,3,5...

2 3cos( / 6) cos( 6)d

ab a bn

Vv v v t n t

Three-Phase Bridge Inverters (cont’d)

The line voltages are six-step waveforms and have characteristic harmonics of 6n1, 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.

Three-Phase Bridge Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

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:

Three-Phase Bridge Inverters (cont’d)

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:

Three-Phase Bridge Inverters (cont’d)

See Bose text for Input Ripple and Device Ratings.

Three-Phase Bridge Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

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 transformer’s secondary windings connected in a wye configuration.

Three-Phase Bridge Inverters (cont’d)

Three-Phase Bridge Inverters (cont’d)

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 .

Three-Phase Bridge Inverters (cont’d)

The transformer’s 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.

0 0 0( )A ad a dv mv m v v

0 0 0( )B be b ev mv m v v

0 0 0( )C cf c fv mv m v v

Three-Phase Bridge Inverters (cont’d)

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 = 6n1 at a phase angle .

0 0AB A Bv v v

0 0BC B Cv v v

0 0CA C Av v v

Three-Phase Bridge Inverters (cont’d)

The Fourier series for vA0 and vB0 are given by:

01,3,5...

4sin cos

2d

An

mV nv n t

n

01,3,5...

4sin cos 2 / 3

2d

Bn

mV nv n t

n

Three-Phase Bridge Inverters (cont’d)

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.

1,5,7,11...

4 2sin cos cos

2 3d

n

mV nn t n t

n

0 0AB A Bv v v

Three-Phase Bridge Inverters (cont’d)

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

Three-Phase Bridge Inverters (cont’d)

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

Three-Phase Bridge Inverters (cont’d)

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.

Three-Phase Bridge Inverters (cont’d)

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

Three-Phase Bridge Inverters (cont’d)

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 = vab+vde-vef

Three-Phase Bridge Inverters (cont’d)

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.

2 3 1 1cos cos5 cos7 ...

5 7d

ab

nVv t t t

2 1 1cos cos 5 cos 7 ...

6 6 5 6 7 63ab d

de

v nVv t t t

25 5 1 5 1 5cos cos 5 cos 7 ...

6 6 5 6 7 63ab d

ef

v nVv t t t

Three-Phase Bridge Inverters (cont’d)

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.

( ) ( ) ( ) ( )

4 3cosd

NA f ab f de f ef f

nVv v v v t

4 3 1 1cos cos11 cos13 ...

11 13d

NA

nVv t t t

Three-Phase Bridge Inverters (cont’d)

See Bose text for 18-step inverter.

Simulating Three-Phase Bridge Inverters

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