Single-Phase Phase-Controlled DC Drives

SECTION 01

Section 1 — Introduction to Single-Phase Drives

Basic Concept

Single-Phase Phase-Controlled DC Drive

A DC motor drive where the armature circuit is connected to the output of a single-phase controlled rectifier using thyristors (SCRs).

Key Operating Principles:

Armature voltage controlled by varying the delay angle $\alpha_a$ of the converter
Field current also controlled using a converter with delay angle $\alpha_f$
Phase-controlled converters use line-commutated thyristors
For improved power factor and reduced harmonics, forced-commutated converters (choppers) can be used

Basic Circuit Arrangement

Important Components:

Smoothing inductor $L_m$ reduces ripple current to acceptable magnitude
Separate converters for armature and field circuits
Essential at low delay angles and high speeds to prevent discontinuous current
Free-wheeling diode (in semiconverter) improves performance

Motor Speed-Torque Relationship

DC Motor Fundamental Equations:

\[V_a = E_b + I_a R_a\]

where $E_b = K_b \phi \omega_m$ is the back EMF.

Speed Equation:

$$\omega_m = \frac{V_a - I_a R_a}{K_b \phi}$$

Torque Equation:

$$T_e = K_t \phi I_a$$

Speed control is achieved by controlling $V_a$ (armature voltage) and $\phi$ (field flux).

SECTION 02

Section 2 — Reversal Techniques

Field and Armature Reversal Methods

Circuit diagram showing field and armature reversals using contactors SW1 and SW2 in both armature and field circuits — Fig. 2 — Field and armature reversals using contactors

Reversal Techniques:

Armature reversal: Using contactors SW1 and SW2 in armature circuit
Field reversal: Using contactors SW1 and SW2 in field circuit

Safety Considerations

Reversal performed at zero armature current to avoid voltage surges
Dead time of 2–10 ms provided to ensure zero current
Field reversal takes longer due to large time constant ($L_f / R_f$)
Only one direction should be reversed at a time

SECTION 03

Section 3 — Types of Single-Phase Drives

Classification of Single-Phase Drives

Single-phase drives can be subdivided into four types:

Single-Phase Half-Wave Converter Drives
- Armature current normally discontinuous
- High ripple content
- Not commonly used in practice
Single-Phase Semiconverter Drives
- One-quadrant operation
- Applications up to 15 kW
- Lower cost, simpler control

Single-Phase Full-Converter Drives
- Two-quadrant operation
- Most commonly used
- Regenerative braking capability
Single-Phase Dual-Converter Drives
- Four-quadrant operation
- Maximum flexibility
- Higher cost and complexity

SECTION 04

Section 4 — Single-Phase Semiconverter Drives

Semiconverter Drive Configuration

Single-phase semiconverter drive circuit showing two thyristors, two diodes, free-wheeling diode, and its first-quadrant operating region — Fig. 3 — Single-phase semiconverter drive circuit and quadrant

Characteristics:

One-quadrant drive (forward motoring only)
Limited to applications up to 15 kW
Two thyristors and two diodes
Free-wheeling diode improves performance and reduces ripple
Current waveforms for highly inductive load

Semiconverter — Voltage Equations

Average Armature Voltage:

$$V_a = \frac{V_m}{\pi}(1 + \cos \alpha_a) \quad \text{for } 0 \leq \alpha_a \leq \pi$$

where $V_m$ is the peak value of the AC supply voltage.

Average Field Voltage (if semiconverter used):

$$V_f = \frac{V_m}{\pi}(1 + \cos \alpha_f) \quad \text{for } 0 \leq \alpha_f \leq \pi$$

Control Range

Delay angle $\alpha_a$ varies from 0 to $\pi$ radians
Voltage can be controlled from $\frac{2V_m}{\pi}$ (at $\alpha_a = 0$) to 0 (at $\alpha_a = \pi$)
Output voltage is always positive (unidirectional)

Semiconverter — Current Analysis

RMS Armature Current:

For continuous conduction mode:

$$I_{a,\text{rms}} = \sqrt{\frac{1}{2\pi}\int_{\alpha_a}^{\pi + \alpha_a} i_a^2 \, d\omega t}$$

Current Ripple:

Peak-to-peak ripple depends on $L_m$, load, and $\alpha_a$
Critical inductance to maintain continuous conduction
Free-wheeling diode reduces negative voltage period

⚠ Important Note

For discontinuous conduction, analysis becomes more complex and average voltage decreases.

SECTION 05

Section 5 — Single-Phase Full-Converter Drives

Full-Converter Drive Configuration

Single-phase full-converter drive circuit with four thyristors in bridge configuration and its two-quadrant operating region — Fig. 4 — Single-phase full-converter drive circuit and quadrant

Characteristics:

Two-quadrant drive (forward motoring and forward braking)
Applications up to 15 kW
Four thyristors in bridge configuration
Armature converter provides $+V_a$ or $-V_a$
Operates in first and fourth quadrants

Full-Converter — Voltage Equations

Average Armature Voltage:

$$V_a = \frac{2V_m}{\pi} \cos \alpha_a \quad \text{for } 0 \leq \alpha_a \leq \pi$$

Average Field Voltage (if full-converter used):

$$V_f = \frac{2V_m}{\pi} \cos \alpha_f \quad \text{for } 0 \leq \alpha_f \leq \pi$$

Advantages over Semiconverter

Can reverse armature voltage polarity
Enables regenerative braking (energy recovery)
Full converter in field circuit can reduce field current faster
Better control range: $-\frac{2V_m}{\pi}$ to $+\frac{2V_m}{\pi}$
Higher efficiency during regeneration

Full-Converter — Quadrant Operation

Operating Modes:

First Quadrant (Motoring): $0 \leq \alpha_a < 90°$
- Positive armature voltage and current
- Motor runs in forward direction
- Power flows from supply to motor
Fourth Quadrant (Regenerative Braking): $90° < \alpha_a \leq 180°$
- Negative armature voltage, positive current direction
- Energy flows back to supply
- Motor acts as generator
- Speed decreases while maintaining same direction

⚠ Extending to Four Quadrants

Reversal of armature terminals or field polarity allows operation in second and third quadrants for complete four-quadrant capability.

Full-Converter — Performance Parameters

RMS Supply Current:

$$I_{s,\text{rms}} = I_a \quad \text{(for continuous conduction)}$$

Input Power Factor:

$$\text{PF} = \frac{V_a I_a}{V_{s,\text{rms}} I_{s,\text{rms}}} = \frac{2\sqrt{2}}{\pi}\cos\alpha_a$$

Harmonic Content:

Dominant harmonics: 2nd, 4th, 6th in output voltage
Supply current harmonics: odd harmonics (3rd, 5th, 7th, etc.)
Total Harmonic Distortion (THD) increases with $\alpha_a$

SECTION 06

Section 6 — Single-Phase Dual-Converter Drives

Dual-Converter Drive Configuration

Single-phase dual-converter drive showing two full-wave converters connected in anti-parallel for four-quadrant operation — Fig. 5 — Single-phase dual-converter drive

Configuration:

Two single-phase full-wave converters connected in anti-parallel
Converter 1: Positive armature voltage $+V_a$
Converter 2: Negative armature voltage $-V_a$
Only one converter operates at a time
Circulating current-free operation

Dual-Converter — Voltage Equations

Converter 1 (Delay angle $\alpha_{a1}$):

$$V_{a1} = \frac{2V_m}{\pi} \cos \alpha_{a1} \quad \text{for } 0 \leq \alpha_{a1} \leq \pi$$

Converter 2 (Delay angle $\alpha_{a2}$):

$$V_{a2} = -\frac{2V_m}{\pi} \cos \alpha_{a2} \quad \text{for } 0 \leq \alpha_{a2} \leq \pi$$

Control Strategy:

$$\alpha_{a2} = \pi - \alpha_{a1}$$

This ensures both converters produce equal and opposite voltages when idle.

Field Voltage (Full converter):

$$V_f = \frac{2V_m}{\pi} \cos \alpha_f \quad \text{for } 0 \leq \alpha_f \leq \pi$$

Dual-Converter — Four-Quadrant Operation

Converter 1 Operation:

First quadrant: Forward motoring ($\alpha_{a1} < 90°$)
Fourth quadrant: Forward regenerative braking ($\alpha_{a1} > 90°$)

Converter 2 Operation:

Second quadrant: Reverse regenerative braking ($\alpha_{a2} > 90°$)
Third quadrant: Reverse motoring ($\alpha_{a2} < 90°$)

Applications

Four-quadrant drive capability without mechanical contactors
Applications up to 15 kW
Suitable for applications requiring frequent reversals
Examples: Rolling mills, hoists, elevators

Dual-Converter — Mode Transition

Switching Between Converters:

Detect zero current crossing in active converter
Provide dead time (2–10 ms)
Block gate pulses to previous converter
Enable gate pulses to new converter

⚠ Circulating Current Issue

If both converters are fired simultaneously:

Large circulating current flows: $i_{\text{circ}} = \frac{V_{a1} - V_{a2}}{R_{\text{eq}}}$
Can damage thyristors
Requires current-limiting reactor in circulating-current mode
Non-circulating mode preferred for lower losses

SECTION 07

Section 7 — Comparison of Drive Types

Comparison of Single-Phase Drive Types

Feature	Semiconverter	Full-Converter	Dual-Converter
Quadrants	1	2	4
Power Range	Up to 15 kW	Up to 15 kW	Up to 15 kW
Thyristors	2	4	8
Voltage Control	$\frac{V_m}{\pi}(1+\cos\alpha_a)$	$\frac{2V_m}{\pi}\cos\alpha_a$	$\frac{2V_m}{\pi}\cos\alpha_a$
Regeneration	No	Yes	Yes
Reversal Method	Mechanical	Field/armature	Converter switching
Complexity	Low	Medium	High
Cost	Lowest	Medium	Highest
Power Factor	Better	Poor at high $\alpha$	Poor at high $\alpha$

Selection Criteria:

Simple unidirectional applications: Semiconverter
Need for regeneration: Full-converter
Frequent reversals without contactors: Dual-converter

SECTION 08

Section 8 — Key Design Considerations

Important Design Considerations

1. Smoothing Inductor Selection:

Connected in series with armature circuit
Minimum inductance: $L_{m,\min} = \frac{V_m R_a}{2\pi f \Delta I_a}$ (approximate)
Reduces ripple current to acceptable magnitude (typically < 10% of rated)
Essential at low delay angles to prevent discontinuous current

2. Field Circuit Design:

Semi- or full-converter for field control
Full converter preferred for faster field current reduction
Large time constant ($\tau_f = L_f/R_f$) affects reversal time
Field forcing for rapid flux changes

3. Protection and Safety:

Zero current detection before reversal
Dead time provision (2–10 ms)
Overvoltage protection (snubber circuits)
Overcurrent protection (fuses, circuit breakers)

Converter Selection for Field Circuit

Semiconverter Option:

Lower cost
Simpler control
Unidirectional power flow
Slower field weakening
Natural commutation only

Full Converter Option:

Higher cost
More complex control
Bidirectional capability
Faster field weakening
Can reverse field voltage

Recommendation

Full converter is preferable for the field circuit due to its ability to reverse voltage polarity and reduce field current much faster than a semiconverter, enabling rapid field weakening for field-weakened operation.

Continuous vs. Discontinuous Conduction

Continuous Conduction Mode (CCM):

Armature current never reaches zero
Occurs when $L_m$ is large or load is heavy
Voltage equations derived earlier are valid
Better performance, lower ripple

Discontinuous Conduction Mode (DCM):

Armature current becomes zero for part of cycle
Occurs when $L_m$ is small or load is light
Average voltage is higher than CCM for same $\alpha_a$
Analysis is more complex
Higher current and voltage ripple

⚠ Design Guideline

Design $L_m$ to ensure continuous conduction at minimum expected load.

SECTION 09

Section 9 — Power Quality and Harmonics

Harmonics in Single-Phase Drives

Output Voltage Harmonics:

Fundamental frequency: $2f$ (for full-wave converters)
Dominant harmonics: $2f$, $4f$, $6f$, etc.
Amplitude decreases with harmonic order
Smoothing inductor filters high-frequency harmonics

Supply Current Harmonics:

Odd harmonics predominate: 3rd, 5th, 7th, 11th, 13th, etc.
$n$-th harmonic current: $I_n \approx \frac{I_1}{n}$
Total Harmonic Distortion: $\text{THD} = \frac{\sqrt{\sum_{n=2}^{\infty} I_n^2}}{I_1}$
Typical THD: 40–80% depending on operating point

Mitigation Techniques

AC line filters
Multi-pulse converters (for higher power ratings)
Active power filters

Power Factor in Phase-Controlled Drives

Displacement Power Factor:

$$\text{DPF} = \cos\phi_1 \approx \cos\alpha_a$$

Distortion Factor:

$$\text{DF} = \frac{I_1}{I_{s,\text{rms}}} = \frac{1}{\sqrt{1 + \text{THD}^2}}$$

Total Power Factor:

$$\text{PF} = \text{DPF} \times \text{DF}$$

⚠ Power Factor Issues

Power factor decreases with increasing $\alpha_a$
At $\alpha_a = 90°$, DPF = 0, no real power transfer
Poor power factor leads to reactive power penalties
Capacitor banks may be required for PF correction

SECTION 10

Section 10 — Summary

Key Takeaways

Single-phase phase-controlled drives use thyristor-based controlled rectifiers to vary DC motor armature voltage
Four main types: half-wave (rarely used), semiconverter (1-quadrant), full-converter (2-quadrant), and dual-converter (4-quadrant)
Smoothing inductor $L_m$ is essential to reduce current ripple and maintain continuous conduction
Field or armature reversal required for opposite direction operation
Safety measures include zero current detection and dead time before reversal
Full-converter preferred for field circuit due to faster current reduction capability
Selection depends on quadrant requirements, power level, and application needs
Power quality concerns: harmonics and poor power factor at high delay angles

Voltage Equation Summary

Drive Type	Armature Voltage	Field Voltage
Semiconverter	$V_a = \dfrac{V_m}{\pi}(1+\cos\alpha_a)$	$V_f = \dfrac{V_m}{\pi}(1+\cos\alpha_f)$
Full-converter	$V_a = \dfrac{2V_m}{\pi}\cos\alpha_a$	$V_f = \dfrac{2V_m}{\pi}\cos\alpha_f$
Dual-converter	$V_a = \pm\dfrac{2V_m}{\pi}\cos\alpha_{a1,2}$	$V_f = \dfrac{2V_m}{\pi}\cos\alpha_f$

All delay angles: $0 \leq \alpha \leq \pi$ radians

Continuous conduction mode assumed

Practical Applications

Typical Applications by Type:

Semiconverter Drives:
- Fans, blowers, pumps
- Conveyors (unidirectional)
- Simple machine tools
Full-Converter Drives:
- Machine tools with regenerative braking
- Printing presses
- Paper and textile mills
Dual-Converter Drives:
- Reversing rolling mills
- Mine hoists and elevators
- Cranes with frequent direction changes