404 - Modular Multilevel Converter¶

Scalable multilevel topology for HVDC and FACTS applications.

Overview¶

The Modular Multilevel Converter (MMC) is the state-of-the-art topology for: - HVDC transmission (±320kV to ±525kV) - STATCOM systems - High-power motor drives - Battery energy storage systems (BESS)

Topology¶

Structure¶

        +Vdc/2
           │
    ┌──────┼──────┐
    │      │      │
   SM     SM     SM   ─── Upper Arm
   SM     SM     SM       (N submodules)
   SM     SM     SM
    │      │      │
    ●──────●──────●  ─── Phase outputs (A, B, C)
    │      │      │
   SM     SM     SM   ─── Lower Arm
   SM     SM     SM       (N submodules)
   SM     SM     SM
    │      │      │
    └──────┼──────┘
           │
        -Vdc/2

Submodule Types¶

Half-Bridge SM:

    ┬───┤S1├───┬
    │         │
    C        out
    │         │
    ┴───┤S2├───┘

Full-Bridge SM:

    ┬───┤S1├───┬───┤S3├───┬
    │         │         │
    C        out        C
    │         │         │
    ┴───┤S2├───┴───┤S4├───┘

Operating Principle¶

Voltage Synthesis¶

• N submodules per arm
• Insert/bypass SMs to create voltage steps
• Output voltage = Vdc/2 - (inserted SMs × Vc)

Current Path¶

• Upper + Lower arm currents combine at output
• Circulating current flows within converter
• Arm inductors limit circulating current

Key Equations¶

Submodule Voltage: $\(V_{SM} = \frac{V_{dc}}{N}\)$

Number of Levels: $\(N_{levels} = N + 1\)$ (per arm)

Arm Current: $\(i_{arm} = \frac{i_{dc}}{3} + \frac{i_{ac}}{2} + i_{circ}\)$

Energy Storage: $\(E_{stored} = 6 \cdot N \cdot \frac{1}{2}CV_{SM}^2\)$

Control Architecture¶

Hierarchical Control¶

1. System Level
2. Active/reactive power control

3. DC voltage control

4. Converter Level

5. Circulating current control

6. Capacitor voltage balancing (average)

7. Arm Level

8. Individual SM capacitor balancing
9. Sorting algorithm (NLM or PWM)

Modulation Methods¶

Nearest Level Modulation (NLM): - Round reference to nearest level - Very low switching frequency - Used in HVDC

Phase-Shifted Carrier PWM: - Higher effective switching frequency - Better harmonic performance - Used in motor drives

Design Parameters¶

Simulation Exercises¶

1. Build 5-level MMC (N=4 per arm)
2. Implement capacitor balancing
3. Compare NLM vs PS-PWM
4. Analyze circulating currents
5. Simulate DC fault response

Applications¶

• HVDC point-to-point links
• Multi-terminal HVDC grids
• Offshore wind connection
• STATCOM for grid support
• Medium-voltage drives
• Railway interties

Related Resources¶

• 403 - NPC Inverter
• 402 - Three-Phase Inverter