Three-Phase Phase-Controlled DC Drives

Why Three-Phase Drives?

Three-phase phase-controlled drives offer significant advantages over their single-phase counterparts, making them the industry standard for medium- to high-power DC motor applications. The key advantages are:

1. Higher Power Ratings: Suitable for $100\;\text{kW}$ to $1500\;\text{kW}$ and beyond.
2. Higher Ripple Frequency:
   • Single-phase full-bridge: ripple at $2f$ (e.g. $120\;\text{Hz}$ for a $60\;\text{Hz}$ supply).
   • Three-phase full-bridge (6-pulse): ripple at $6f$ (e.g. $360\;\text{Hz}$ for a $60\;\text{Hz}$ supply).
3. Lower Filtering Requirements: Smaller smoothing inductor required for the same current-ripple specification.
4. Better Motor Performance: More continuous armature current leads to smoother torque.
5. Lower Torque Pulsation: Smoother shaft torque reduces mechanical stress.
6. Higher Efficiency: Better utilisation of transformer and supply capacity.

Power Ranges for Different DC Drive Topologies

Classification of Three-Phase Drives

Based on converter configuration, three-phase drives are classified as follows:

1. Three-Phase Half-Wave (3-pulse) Converter: Requires a neutral connection; rarely used industrially.
2. Three-Phase Semiconverter (half-controlled bridge): One-quadrant operation (forward motoring only); up to $115\;\text{kW}$.
3. Three-Phase Full-Converter (fully-controlled bridge): Two-quadrant operation (motoring + regenerative braking); up to $1500\;\text{kW}$.
4. Three-Phase Dual-Converter: Four-quadrant operation; up to $1500\;\text{kW}$.

Three-Phase Supply — Notation

The standard three-phase system with phase sequence $a$-$b$-$c$ is described by the phase voltages of a Y-connected supply:

$$v_a = V_m \sin\omega t$$ $$v_b = V_m \sin\!\bigl(\omega t - 120°\bigr)$$ $$v_c = V_m \sin\!\bigl(\omega t - 240°\bigr)$$

where $V_m = \sqrt{2}\,V_p$ is the peak phase voltage and $V_{Lm} = \sqrt{2}\,V_L = \sqrt{3}\,V_m$ is the peak line-to-line voltage. The fundamental relation is $V_L = \sqrt{3}\,V_p$.

Ripple Frequency Comparison

Key Observation:

• Single-phase bridge (2-pulse): ripple period $= T/2$, ripple frequency $= 2f$
• Three-phase bridge (6-pulse): ripple period $= T/6$, ripple frequency $= 6f$

Consequence

A six times higher ripple frequency means the peak-to-peak voltage ripple is much smaller, so a smaller smoothing inductor $L_a$ is needed for the same current-ripple specification.

Circuit Diagram

Operating Principle

Positive Group — Thyristors $T_1, T_3, T_5$:

• Each thyristor is fired with a common delay angle $\alpha$ after its respective phase voltage becomes the most positive.
• Provides the high-potential rail of the output.

Negative Group — Diodes $D_4, D_6, D_2$:

• Diodes conduct naturally (no delay) on the most negative phase.
• Provides the low-potential rail.

Freewheeling Diode $D_F$:

• Conducts whenever the instantaneous converter output would go negative.
• Clamps $v_o \geq 0$ and maintains continuous armature current.
• Reduces current ripple and protects the motor from negative voltage transients.

Voltage and Current Waveforms

Average Output Voltage

The average armature voltage for a three-phase semiconverter is given by:

where $V_m = \sqrt{2}\,V_p$ is the peak phase voltage. An equivalent expression in terms of the line voltage $V_L$ is:

since $\sqrt{3}\,V_m = V_{Lm} = \sqrt{2}\,V_L$.

Advantages and Disadvantages

Circuit Diagram

Thyristor Firing and Conduction

The bridge structure consists of:

• Positive group: $T_1$ (phase $a$), $T_3$ (phase $b$), $T_5$ (phase $c$)
• Negative group: $T_4$ (phase $a$), $T_6$ (phase $b$), $T_2$ (phase $c$)

The firing sequence is $T_1$–$T_2$–$T_3$–$T_4$–$T_5$–$T_6$, with each thyristor separated by $60°$ and conducting for $120°$.

Output Voltage Waveforms

Average Output Voltage

In terms of the RMS line voltage $V_L$:

Two-Quadrant Operation

Quadrant I — Forward Motoring:

• $\alpha < 90° \Rightarrow V_a > 0$, $\;I_a > 0$
• $V_a > E_b$ (back-EMF)
• Power flow: Supply → Motor

Quadrant II — Forward Regenerative Braking:

• $\alpha > 90° \Rightarrow V_a < 0$, $\;I_a > 0$
• Motor still rotates forward ($E_b > 0$)
• $E_b > |V_a|$ drives current in the same direction
• Power flow: Motor → Supply

Important Note

Thyristors carry current in one direction only; it is the voltage $V_a$ that reverses, not $I_a$.

Regenerative Braking

Physical Mechanism:

• Motor is running forward; the load (or flywheel) has stored kinetic energy.
• Delay angle is increased beyond $90°$: converter output voltage $V_a$ becomes negative.
• Back-EMF $E_b$ (still positive) now exceeds $|V_a|$.
• Armature current $I_a$ continues to flow in the same (positive) direction.
• Instantaneous power $P = V_a \cdot I_a < 0$: energy flows from motor back to the AC supply.
• Motor decelerates — kinetic energy is returned to the grid.

Step-by-Step Transition from Motoring to Regeneration:

1. Motor running in forward motoring mode: $\alpha < 90°$
2. Controller gradually increases $\alpha$ toward $90°$
3. At $\alpha = 90°$: $V_a = 0$; motor runs on stored energy
4. $\alpha$ is further increased beyond $90°$: $V_a$ becomes negative
5. Back-EMF $E_b$ (still positive) drives $I_a$ in the original direction
6. Power reverses — motor begins to decelerate; energy returns to supply

Input Power Factor

For perfectly smooth (continuous) armature current $I_a$, each supply line carries $+I_a$ for $120°$ and $-I_a$ for $120°$ per cycle, giving an RMS line current of:

The input displacement power factor is then:

Field Circuit

The field circuit of a DC motor has a large time constant $\tau_f = L_f / R_f$. Using a full-converter for the field supply enables the following:

• A full-converter can apply negative voltage across the field winding, actively forcing the field current down faster.
• This reduces the time required for field reversal (important for four-quadrant drives) and for field weakening at high speed.

The field voltage supplied by a three-phase full-converter is:

Speed Control Regions

Region 1 — Below Base Speed ($0$ to $N_{\text{base}}$):

• Field current held at rated value $I_{f,\text{rated}}$.
• Speed is varied by changing $\alpha_a$ — armature voltage control.
• Torque capability: constant (rated torque).

Region 2 — Above Base Speed ($N > N_{\text{base}}$):

• Armature voltage at maximum ($\alpha_a = 0°$).
• Speed is increased by reducing field current — field weakening.
• Torque capability: inversely proportional to speed (constant power operation).

Typical Applications

The full-converter drive is used in industrial applications that require two-quadrant control:

Circuit Diagram

Operating Principle

• Converter P active ⟹ Quadrants I and II
  • Forward motoring (Q-I): $\;\alpha_P < 90° \Rightarrow V_a > 0$
  • Forward regeneration (Q-II): $\;\alpha_P > 90° \Rightarrow V_a < 0$
• Converter N active ⟹ Quadrants III and IV
  • Reverse motoring (Q-III): $\;\alpha_N < 90° \Rightarrow V_a < 0$
  • Reverse regeneration (Q-IV): $\;\alpha_N > 90° \Rightarrow V_a > 0$

Voltage Equations and Constraint

The average output voltage of each converter is:

For simultaneous operation without short-circuit, the following constraint must be maintained:

This ensures $V_N = -V_P$, so the motor terminal voltage (which is $-V_N$ for Converter N) equals $V_P$. Both converters therefore agree on the motor terminal voltage in the average sense, while only one carries the load current at any time.

Four-Quadrant Summary

Non-Circulating Current Mode

This is the preferred operating mode in modern drives:

• Only one converter conducts at a time; the other is fully blocked (all gate pulses removed).
• A dead time (typically $2$–$10\;\text{ms}$) is inserted between switching to allow the outgoing converter's current to fall to zero.
• No inter-group reactor is needed.

Switching Sequence (Converter P → Converter N):

1. Ramp $\alpha_P$ to reduce $I_a$ smoothly toward zero.
2. Wait for dead time; detect zero current.
3. Block all gate pulses to Converter P.
4. Enable gate pulses to Converter N with appropriate $\alpha_N$.

Circulating Current Mode

In this mode, both converters are enabled simultaneously at all times with the constraint $\alpha_P + \alpha_N = 180°$ maintained. An inter-group reactor $L_r$ is connected between the two converter outputs to limit the circulating current.

Because $v_P + v_N \neq 0$ at every instant (only the averages cancel), a time-varying voltage appears across $L_r$, driving a circulating current:

Field Circuit for Dual-Converter Drives

A single-phase or three-phase full-converter is recommended for the field supply:

• Provides two-quadrant field control (positive and negative $V_f$).
• Enables fast field reversal — essential for four-quadrant reversing drives.
• A single-phase full-converter is usually adequate (field power ≪ armature power).

Advantages and Disadvantages

Single-Phase vs. Three-Phase DC Drives

Comparison of Three-Phase Converter Types

Drive Selection Guide

Key Equations at a Glance

Summary Points

1. Three-phase converters offer higher power capacity, lower ripple ($6f$), and better efficiency than single-phase counterparts, making them the industry standard for medium- to high-power DC drives.
2. Semiconverter: One-quadrant operation ($V_a \geq 0$ always); uses a freewheeling diode; suitable for simple unidirectional loads with no regeneration requirement.
3. Full-converter: Two-quadrant operation (motoring + regenerative braking); the workhorse of industrial DC drives; $V_a$ can be positive or negative by varying $\alpha$ from $0°$ to $180°$.
4. Dual-converter: Four-quadrant operation by anti-parallel connection of two full-converters; enables fast electronic reversal; non-circulating current mode is preferred.
5. Speed control: Below base speed uses armature voltage control (constant torque region); above base speed uses field weakening (constant power region).
6. Field converter: Should be a full-converter (or better) for any drive that requires fast field reversal or field weakening above base speed.