Dual Converters

Single-Phase Controlled Rectifiers

Introduction to Converter Quadrants

One Quadrant Converters

Characteristics:

  • Output voltage (\(V_o\)) and output current (\(I_o\)) maintain the same polarity throughout the entire firing angle control range

  • Also known as first quadrant converters

  • Unidirectional power flow: from AC source to DC load

Example: Semi-Converters

  • Both \(V_o\) and \(I_o\) are positive

  • Operate exclusively in rectifier mode

  • Power flows from AC source to DC load

Two Quadrant Converters

Operating Modes:

Rectifier Mode

  • \(V_o\) and \(I_o\) have same polarity

  • Firing angle: \(0 \leq \alpha \leq \frac{\pi}{2}\)

  • First quadrant operation

  • Power: AC source \(\rightarrow\) DC load

Inverter Mode

  • \(V_o\) and \(I_o\) have opposite polarity

  • Firing angle: \(\frac{\pi}{2} \leq \alpha \leq \pi\)

  • Fourth quadrant operation

  • Power: DC load \(\rightarrow\) AC source

Key Feature

Enables bidirectional power flow with unidirectional current

Full Converters - Two Quadrant Operation

Properties:

  • Operate in I-quadrant and IV-quadrant

  • Current direction fixed (unidirectional thyristors)

  • Voltage polarity reversible

First Quadrant

  • \(V_o > 0\), \(I_o > 0\)

  • \(0 \leq \alpha \leq \frac{\pi}{2}\)

  • Controlled rectifier

  • Power: AC \(\rightarrow\) DC

Fourth Quadrant

  • \(V_o < 0\), \(I_o > 0\)

  • \(\frac{\pi}{2} \leq \alpha \leq \pi\)

  • Line commutated inverter

  • Power: DC \(\rightarrow\) AC

Four Quadrant Operation

DC Motor Operation Modes:

  1. Forward motoring (Quadrant I)

  2. Forward regeneration (Quadrant II)

  3. Reverse motoring (Quadrant III)

  4. Reverse regeneration (Quadrant IV)

Four quadrant operation of converters
Four quadrant operation of converters

Requirement

Four quadrant converters needed for complete DC motor control

Dual Converters

What are Dual Converters?

Definition

Dual converters consist of two fully controlled converters connected in anti-parallel (back-to-back) configuration to the load circuit.

Key Features:

  • Enable four-quadrant operation

  • Bidirectional voltage and current capability

  • Essential for reversible DC motor drives

(a) Dual converter configuration (b) Four quadrant operation
(a) Dual converter configuration (b) Four quadrant operation

Operating Principle of Ideal Dual Converter

Equivalent Circuit Components

Basic Circuit Elements:

  • Two ideal two-quadrant converters (Converter-1 and Converter-2)

  • Two diodes (\(D_1\) and \(D_2\)) representing unidirectional current flow

  • Load (typically DC motor with back EMF and inductance)

Equivalent circuit of an ideal dual converter
Equivalent circuit of an ideal dual converter

Equivalent Model:

  • Converters modeled as controllable DC voltage sources

  • Diodes in series ensure unidirectional current capability

Assumptions for Analysis

Ideal Conditions:

  1. Converters are ideal full converters

  2. No ripple in output voltage (pure DC)

  3. Negligible converter losses

  4. Diodes \(D_1\) and \(D_2\) allow bidirectional current flow

  5. Firing angles controlled by control voltage \(V_C\)

Note

These assumptions simplify analysis and help understand fundamental operating principles.

Output Voltage Relations

Voltage Characteristics:

  • \(V_{o1}\) and \(V_{o2}\): average output voltages of Converter-1 and Converter-2

  • Equal in magnitude but opposite in polarity

  • Drive current in opposite directions through the load

Operating Principle:

  • When one converter operates as controlled rectifier, the other operates as inverter

  • Positive group converter: Functions as rectifier

  • Negative group converter: Functions as inverter

Mathematical Relations

Average Output Voltages:

\[\begin{aligned} V_{o1} &= V_{\max} \cos \alpha_1 \\ V_{o2} &= V_{\max} \cos \alpha_2 \end{aligned}\]

where for a single-phase full converter:

\[V_{\max} = \frac{2\sqrt{2}V}{\pi}\]

For an ideal converter: \(V_o = V_{o1} = -V_{o2}\)

\[\begin{aligned} V_{\max} \cos \alpha_1 &= -V_{\max} \cos \alpha_2 \\ \cos \alpha_1 &= -\cos \alpha_2 = \cos(180° - \alpha_2) \end{aligned}\]

Fundamental Equation

\[\boxed{\alpha_1 + \alpha_2 = 180°}\]

Firing Angle Control

Control Strategy:

  • Firing angles varied maintaining: \(\alpha_1 + \alpha_2 = 180°\)

  • Ensures equal magnitude but opposite polarity voltages

Terminal voltage variation with firing angle for ideal dual converter
Terminal voltage variation with firing angle for ideal dual converter

Example:

  • If \(\alpha_1 = 30°\) \(\Rightarrow\) \(\alpha_2 = 150°\)

    • Converter-1: Rectifier mode

    • Converter-2: Inverter mode

Practical Dual Converter

Issues in Practical Dual Converter

Challenge: Although average voltages are equal and opposite, instantaneous voltages differ.

Consequences:

  • Instantaneous output voltages \(V_{o1}\) and \(V_{o2}\) are out of phase

  • Voltage difference exists between the two converters

  • Large circulating current flows between converters (not through load)

Solutions:

  1. Insert a reactor between converters to limit circulating current

  2. Provide appropriate trigger pulses to avoid circulating current

Operating Modes

Two Operating Modes of Practical Dual Converter

Mode 1

Non-Circulating Current Mode
One converter active at a time

Mode 2

Circulating Current Mode
Both converters active simultaneously

Non-Circulating Current Mode

Operating Principle

Key Characteristics:

  • Only one converter operates at any given time

  • Operating converter carries entire load current

  • Active converter receives firing pulses from triggering circuit

  • Idle converter blocked by removing triggering pulses

  • No circulating current flows

  • Reactor not required

Advantage

Eliminates circulating current losses and reactor cost

Circuit Configuration

(a) Non-circulating current mode dual converter with generic load (b) Non-circulating current mode dual converter with DC motor
(a) Non-circulating current mode dual converter with generic load (b) Non-circulating current mode dual converter with DC motor

Converter Switching Process

Switching from Converter-1 to Converter-2:

  1. Step 1: Remove firing pulses to thyristors of Converter-1
    (OR increase firing angle \(\alpha_1\) to maximum value)

  2. Step 2: Load current decays to zero

  3. Step 3: Wait for delay time (10–20 ms)

  4. Step 4: Apply triggering pulses to thyristors of Converter-2

  5. Step 5: Converter-2 switches ON

  6. Step 6: Load current builds up in opposite direction

Critical Requirement

Delay time ensures reliable commutation of thyristors

Delay Time Requirement

Purpose of Delay Time:

  • Delay time: typically 10 to 20 ms

  • Delay between instant when Converter-1 turns OFF and Converter-2 turns ON

  • Ensures reliable commutation of all thyristors in Converter-1

Consequence of Insufficient Delay

If Converter-2 is triggered before Converter-1 completely turns off:

  • Large circulating current flows between converters

  • Potential damage to thyristors

  • System instability

Load Current Characteristics

Current Modes:

  • Load current may be continuous or discontinuous

  • Depends on load inductance and firing angle

Control Circuit Design:

  • Must provide satisfactory performance during both modes:

    • Continuous load current operation

    • Discontinuous load current operation

  • Proper current sensing and feedback mechanisms required

Circulating Current Mode

Operating Principle

Key Characteristics:

  • Both converters in operating condition simultaneously

  • One converter operates in controlled rectifier mode

  • Other operates in inverting mode

  • Reactor inserted between Converter-1 and Converter-2

  • Reactor limits amplitude of circulating current to acceptable value

Circulating current mode dual converter with reactor
Circulating current mode dual converter with reactor

Firing Angle Control

Control Law: \(\alpha_1 + \alpha_2 = 180°\) always satisfied

Example: If \(\alpha_1 = 45°\), then \(\alpha_2 = 135°\)

  • Converter-1 operates as controlled rectifier (\(\alpha_1 < 90°\))

  • Converter-2 operates as inverter (\(\alpha_2 > 90°\))

Voltage Characteristics:

  • Average values of \(V_{o1}\) and \(V_{o2}\) are equal

  • Instantaneous values of \(V_{o1}\) and \(V_{o2}\) differ

  • Voltage difference causes circulating current

Critical Component

Reactor (inductor) is essential to limit circulating current

Voltage Waveforms

Voltage waveforms of a single-phase dual converter in circulating current mode
Voltage waveforms of a single-phase dual converter in circulating current mode

Load Current Reversal

Reversal Process:

  • Load current reversed by interchanging roles of two converters

  • Converter-1 switches to inverter mode (\(\alpha_1 > 90°\))

  • Converter-2 switches to rectifier mode (\(\alpha_2 < 90°\))

  • Equation \(\alpha_1 + \alpha_2 = 180°\) always satisfied

Advantage

  • Normal delay time (10–20 ms) not required

  • Instantaneous current reversal possible

  • Operation of this type of dual converter is faster

  • Better dynamic response

Comparison of Operating Modes

Non-Circulating vs Circulating Current Mode

Parameter Non-Circulating Circulating
Converters active One at a time Both simultaneously
Circulating current Zero Present
Reactor required No Yes
Switching delay 10–20 ms Negligible
Response speed Slower Faster
Efficiency Higher Lower
THD rating Lower Higher
Cost Lower Higher

Disadvantages of Dual Converters

Disadvantages

Major Drawbacks:

  1. Reactor size and cost

    • Required to limit circulating current

    • Size and cost significantly high at high power levels

    • Adds weight and volume to the system

  2. Low efficiency and power factor

    • Due to losses from circulating current

    • Increased copper and core losses in reactor

  3. Higher thyristor current rating

    • Must handle both load current and circulating current

    • Increases device cost

  4. Complex control system

    • Requires precise firing angle coordination

When to Use Circulating Current Mode

Despite disadvantages, circulating current mode dual converter is preferred when:

Application Requirements

  • Load current needs to be reversed frequently

  • Fast response four-quadrant operation is required

  • Dynamic performance is critical

  • No time delay can be tolerated during reversal

Typical Applications:

  • Reversible rolling mill drives

  • High-performance servo systems

  • Rapid transit systems

Summary

Key Points

  1. Dual converters enable four-quadrant operation for DC motor drives

  2. Consist of two fully controlled converters connected back-to-back

  3. Fundamental relation for ideal dual converter: \(\boxed{\alpha_1 + \alpha_2 = 180°}\)

  4. Two operating modes available:

    • Non-circulating current mode: One converter active, no reactor

    • Circulating current mode: Both converters active, reactor required

  5. Non-circulating mode: Higher efficiency, slower response

  6. Circulating mode: Faster response, higher losses

  7. Choice depends on application requirements

  8. Essential for reversible DC motor control applications