Module 5 · Controlled Rectifiers

Dual Converters

Four-Quadrant Operation: Circulating and Non-Circulating Current Modes

Dr. Mithun Mondal BITS Pilani EEE — Power Electronics
01

One Quadrant Converters

Characteristics:

Example: Semi-Converters

02

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

03

Full Converters - Two Quadrant Operation

Properties:

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

04

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

05

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
06

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:

07

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.

08

Output Voltage Relations

Voltage Characteristics:

Operating Principle:

09

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
\[\boxed{\alpha_1 + \alpha_2 = 180°}\]
10

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:

11

Issues in Practical Dual Converter

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

Consequences:

Solutions:

  1. Insert a reactor between converters to limit circulating current

  2. Provide appropriate trigger pulses to avoid circulating current

12

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

13

Operating Principle

Key Characteristics:

Advantage

Eliminates circulating current losses and reactor cost

14

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
15

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

16

Delay Time Requirement

Purpose of Delay Time:

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

17

Load Current Characteristics

Current Modes:

Control Circuit Design:

18

Operating Principle

Key Characteristics:

Circulating current mode dual converter with reactor
Circulating current mode dual converter with reactor
19

Firing Angle Control

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

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

Voltage Characteristics:

Critical Component

Reactor (inductor) is essential to limit circulating current

20

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
21

Load Current Reversal

Reversal Process:

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

22

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
23

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

24

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:

25

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