Dual Converters

Dual converters represent the highest level of control flexibility in thyristor-based DC drives, enabling true four quadrant operation of DC motors. By combining two fully controlled converters connected in anti-parallel to the same load, dual converters allow the output voltage polarity and current direction to be reversed independently. This makes them indispensable in demanding applications such as reversible rolling mills, mine hoists, and precision servo systems where rapid reversal of motor direction and regenerative braking are essential.

Core Concept Explanation

A dual converter consists of two fully controlled converters connected in anti-parallel across the same DC load. Converter P (positive converter) provides positive output voltage and positive current (forward motoring and reverse braking). Converter N (negative converter) provides negative output voltage and positive current (reverse motoring and forward braking). Together, they allow operation in all four quadrants of the V-I plane, which no single converter can achieve.

The anti-parallel connection means the output terminals of Converter P and Converter N are connected with opposite polarity. If both converters were allowed to produce different voltages simultaneously, a large short circuit current would flow between them. To prevent this, the fundamental constraint of dual converter operation must be satisfied: αP + αN = 180°. This ensures that both converters always tend to produce the same magnitude of output voltage (with opposite sign), so no net voltage difference drives a circulating current.

There are two operating modes for dual converters. In circulating current mode, both converters operate simultaneously. A center tapped inter-group reactor (IGR) is connected between the two converters to limit the circulating current that flows due to instantaneous voltage differences between the converters (even though average voltages are equal, instantaneous ripple voltages differ). This mode offers fast response and continuous control but requires the reactor, which adds cost and bulk.

In circulating current free mode, only one converter operates at a time. A current sensing circuit detects when the load current crosses zero, and firing pulses to the active converter are blocked before firing pulses to the other converter are enabled. A dead time of 10 to 20 milliseconds is introduced to ensure no overlap. This mode eliminates the IGR but has slower dynamic response.

Mathematical Expression

The constraint equation αP + αN = 180° is the governing relation for dual converters. If Converter P is set to αP = 60° (giving positive Vdc), then Converter N must be set to αN = 120° (giving negative Vdc of same magnitude, operating in inverting mode). The output voltages are Vdc_P = Vdo × cos αP and Vdc_N = Vdo × cos αN = Vdo × cos(180° - αP) = -Vdo × cos αP. Since both converters are connected anti-parallel, the actual voltage seen by the load is the same in both cases, confirming no net voltage drives a steady circulating current.

The circulating current in circulating current mode is limited by the inter-group reactor inductance L. The circulating current ic flows in a loop through both converters and the IGR. The instantaneous voltage driving this current is the difference of instantaneous output voltages of the two converters, which has a ripple frequency related to the pulse number. A larger IGR inductance limits ic to a smaller value but increases the cost and physical size.

Practical Understanding

In reversible DC motor drives, the four quadrant capability is directly mapped to motor operation. Quadrant 1 is forward motoring (positive speed, positive torque), Quadrant 2 is forward regenerative braking (positive speed, negative torque), Quadrant 3 is reverse motoring (negative speed, negative torque), and Quadrant 4 is reverse regenerative braking (negative speed, positive torque). A reversible rolling mill, for example, must accelerate the rolls forward, brake regeneratively, and then drive them in reverse in rapid succession, requiring full four quadrant control.

The inter-group reactor in circulating current mode is physically a center-tapped inductor or two separate inductors. It must carry full load current in addition to the circulating current. In practical designs, the circulating current is limited to 10 to 15 percent of rated current to keep reactor size manageable while still maintaining the speed advantage of continuous conduction in both converters.

Given:
Dual converter using 6-pulse bridges
Line voltage VL = 415 V (rms), αP = 45°
Constraint: αP + αN = 180°
Find: αN and both converter output voltages

Why this formula applies:
Dual converter constraint ensures equal average voltage magnitudes.
Vdc = 2.34 × VL_rms × cosα for each 6-pulse bridge.

Formula:
αN = 180° - αP
Vdc_P = 2.34 × VL × cos αP
Vdc_N = 2.34 × VL × cos αN

Substitution:
αN = 180° - 45° = 135°
Vdc_P = 2.34 × 415 × cos 45° = 970.5 × 0.707 = 686.2 V
Vdc_N = 2.34 × 415 × cos 135° = 970.5 × (-0.707) = -686.2 V

Calculation:
Vdc_P = +686.2 V (positive, forward motoring)
Vdc_N = -686.2 V (negative, would drive reverse current)

Final Answer: Load sees Vdc = 686.2 V. αN = 135°.

Exam Tip: The constraint αP + αN = 180° is the single most tested fact about dual converters in GATE. Also remember: in circulating current free mode, both converters cannot be ON simultaneously — there is always a dead time. In circulating current mode, the inter-group reactor limits (but does not eliminate) circulating current.

Four Quadrant Summary

• Q1: Vdc positive, Id positive. Converter P active (αP < 90°). Forward motoring.
• Q2: Vdc negative, Id positive. Converter N active in inverting mode (αN > 90°). Forward regenerative braking.
• Q3: Vdc negative, Id negative. Converter N active (αN < 90°). Reverse motoring.
• Q4: Vdc positive, Id negative. Converter P active in inverting mode (αP > 90°). Reverse regenerative braking.
• Circulating current mode: IGR required. Both converters always active. Fast dynamic response.
• Circulating current free mode: No IGR. Dead time of 10–20 ms. One converter at a time.

Quick Revision

• Dual converter = two fully controlled converters in anti-parallel across same load.
• Constraint: αP + αN = 180°. This is the fundamental operating condition.
• Four quadrant operation: forward/reverse motoring and forward/reverse regenerative braking.
• Circulating current mode: both ON, IGR limits circulating current, fast response.
• Circulating current free mode: one ON at a time, dead time needed, no IGR required.
• Exam trap: αP + αN ≠ 180° means unequal voltages → large circulating current → converter damage.
• Circulating current exists even when average voltages are equal, due to instantaneous ripple voltage differences.