Modular Multilevel Converters (MMCs)

1. Definition and Core Principles

1.1 Definition and Core Principles

A Modular Multilevel Converter (MMC) is a power electronic topology used in high-voltage direct current (HVDC) transmission and flexible AC transmission systems (FACTS). Unlike conventional two-level or three-level converters, an MMC employs a cascaded arrangement of identical submodules (SMs), enabling near-sinusoidal output voltages with reduced harmonic distortion and lower switching losses.

Topology and Submodule Structure

The fundamental building block of an MMC is the submodule, typically implemented as a half-bridge or full-bridge converter with a floating capacitor. For a half-bridge SM, the output voltage VSM can be either VC (capacitor voltage) or 0, depending on the switching state:

$$ V_{SM} = S \cdot V_C $$

where S is the switching function (0 or 1). A full-bridge SM extends this capability to ±VC, enabling fault blocking and enhanced control flexibility.

Arm Configuration and Voltage Synthesis

An MMC phase leg consists of upper and lower arms, each containing N series-connected SMs and an arm inductor Larm. The total DC-link voltage VDC is distributed across the arms, with the output phase voltage synthesized by modulating the number of inserted SMs in each arm. The instantaneous output voltage Vph is:

$$ V_{ph} = \frac{V_{DC}}{2} - \left( \frac{N - n_{upper}}{N} \right) V_{DC} $$

where nupper is the number of inserted SMs in the upper arm. The arm inductor suppresses circulating currents and balances energy distribution among SMs.

Capacitor Voltage Balancing

Maintaining capacitor voltage equilibrium is critical for stable operation. A sorting algorithm dynamically selects SMs based on:

For a half-bridge SM, the capacitor current iC is:

$$ i_C = S \cdot i_{arm} $$

where iarm is the arm current. Energy balancing ensures that all capacitors converge to VC = VDC/N.

Advantages Over Conventional Converters

MMCs dominate modern HVDC projects (e.g., Siemens’ HVDC PLUS, ABB’s HVDC Light) due to their efficiency (>98%) and compatibility with renewable energy integration.

MMC Phase Leg SM1
MMC Phase Leg Topology with Submodules Schematic of a Modular Multilevel Converter (MMC) phase leg showing upper and lower arms with series-connected submodules (SMs), arm inductors, DC-link, and output phase terminal. V_DC Upper Arm SM1 SM2 ... SMN L_arm Lower Arm SM1 SM2 ... SMN L_arm V_ph S S S S
Diagram Description: The diagram would physically show the cascaded arrangement of submodules (SMs) in upper/lower arms, their connection to the DC-link, and the role of arm inductors.

1.1 Definition and Core Principles

A Modular Multilevel Converter (MMC) is a power electronic topology used in high-voltage direct current (HVDC) transmission and flexible AC transmission systems (FACTS). Unlike conventional two-level or three-level converters, an MMC employs a cascaded arrangement of identical submodules (SMs), enabling near-sinusoidal output voltages with reduced harmonic distortion and lower switching losses.

Topology and Submodule Structure

The fundamental building block of an MMC is the submodule, typically implemented as a half-bridge or full-bridge converter with a floating capacitor. For a half-bridge SM, the output voltage VSM can be either VC (capacitor voltage) or 0, depending on the switching state:

$$ V_{SM} = S \cdot V_C $$

where S is the switching function (0 or 1). A full-bridge SM extends this capability to ±VC, enabling fault blocking and enhanced control flexibility.

Arm Configuration and Voltage Synthesis

An MMC phase leg consists of upper and lower arms, each containing N series-connected SMs and an arm inductor Larm. The total DC-link voltage VDC is distributed across the arms, with the output phase voltage synthesized by modulating the number of inserted SMs in each arm. The instantaneous output voltage Vph is:

$$ V_{ph} = \frac{V_{DC}}{2} - \left( \frac{N - n_{upper}}{N} \right) V_{DC} $$

where nupper is the number of inserted SMs in the upper arm. The arm inductor suppresses circulating currents and balances energy distribution among SMs.

Capacitor Voltage Balancing

Maintaining capacitor voltage equilibrium is critical for stable operation. A sorting algorithm dynamically selects SMs based on:

For a half-bridge SM, the capacitor current iC is:

$$ i_C = S \cdot i_{arm} $$

where iarm is the arm current. Energy balancing ensures that all capacitors converge to VC = VDC/N.

Advantages Over Conventional Converters

MMCs dominate modern HVDC projects (e.g., Siemens’ HVDC PLUS, ABB’s HVDC Light) due to their efficiency (>98%) and compatibility with renewable energy integration.

MMC Phase Leg SM1
MMC Phase Leg Topology with Submodules Schematic of a Modular Multilevel Converter (MMC) phase leg showing upper and lower arms with series-connected submodules (SMs), arm inductors, DC-link, and output phase terminal. V_DC Upper Arm SM1 SM2 ... SMN L_arm Lower Arm SM1 SM2 ... SMN L_arm V_ph S S S S
Diagram Description: The diagram would physically show the cascaded arrangement of submodules (SMs) in upper/lower arms, their connection to the DC-link, and the role of arm inductors.

1.2 Historical Development and Evolution

Early Concepts and Theoretical Foundations

The origins of Modular Multilevel Converters (MMCs) trace back to the 1960s with the advent of voltage-source converters (VSCs). The foundational concept of cascading multiple submodules to achieve high-voltage operation was first proposed by McMurray in 1970, who introduced the idea of series-connected switching cells for harmonic mitigation. However, practical implementation was limited by the lack of high-power semiconductor devices and control complexities.

In the 1980s, the emergence of insulated-gate bipolar transistors (IGBTs) enabled more efficient multilevel topologies. The flying capacitor and diode-clamped converters dominated early research, but their scalability issues for high-voltage direct current (HVDC) applications spurred interest in modular designs. The theoretical framework for MMCs was formalized in 2003 by Marquardt and Lesnicar, who introduced the concept of distributed capacitor energy storage and redundant submodules for fault tolerance.

Key Milestones in MMC Development

Technological Advancements and Modern Applications

The evolution of MMCs has been driven by three critical advancements:

  1. Control Algorithms: Transition from centralized PWM to distributed capacitor voltage balancing, enabled by high-speed DSPs.
  2. Semiconductor Technology: Shift from IGBTs to wide-bandgap devices (SiC/GaN), reducing switching losses by up to 30%.
  3. Topology Innovations: Development of arm-inductor-less designs and modular matrix converters for medium-voltage applications.

Modern MMCs now dominate HVDC transmission, renewable energy integration, and grid-forming inverters. Projects like the 1.1 GW DolWin6 (Germany) and the 3 GW Xiluodo (China) showcase their scalability. Research continues into solid-state transformer integrations and AI-based predictive maintenance.

Mathematical Underpinnings of Early MMC Control

The fundamental voltage balancing equation for a submodule capacitor, derived from energy conservation principles, is:

$$ \frac{dV_{sm}}{dt} = \frac{i_{arm}}{C_{sm}} \cdot S $$

where Vsm is the submodule capacitor voltage, iarm the arm current, Csm the capacitance, and S the switching state (0 or 1). Early control systems relied on linearized approximations of this nonlinear relationship.

Evolution of MMC Submodule Count in HVDC Projects 2010 2014 2018 2022

1.2 Historical Development and Evolution

Early Concepts and Theoretical Foundations

The origins of Modular Multilevel Converters (MMCs) trace back to the 1960s with the advent of voltage-source converters (VSCs). The foundational concept of cascading multiple submodules to achieve high-voltage operation was first proposed by McMurray in 1970, who introduced the idea of series-connected switching cells for harmonic mitigation. However, practical implementation was limited by the lack of high-power semiconductor devices and control complexities.

In the 1980s, the emergence of insulated-gate bipolar transistors (IGBTs) enabled more efficient multilevel topologies. The flying capacitor and diode-clamped converters dominated early research, but their scalability issues for high-voltage direct current (HVDC) applications spurred interest in modular designs. The theoretical framework for MMCs was formalized in 2003 by Marquardt and Lesnicar, who introduced the concept of distributed capacitor energy storage and redundant submodules for fault tolerance.

Key Milestones in MMC Development

Technological Advancements and Modern Applications

The evolution of MMCs has been driven by three critical advancements:

  1. Control Algorithms: Transition from centralized PWM to distributed capacitor voltage balancing, enabled by high-speed DSPs.
  2. Semiconductor Technology: Shift from IGBTs to wide-bandgap devices (SiC/GaN), reducing switching losses by up to 30%.
  3. Topology Innovations: Development of arm-inductor-less designs and modular matrix converters for medium-voltage applications.

Modern MMCs now dominate HVDC transmission, renewable energy integration, and grid-forming inverters. Projects like the 1.1 GW DolWin6 (Germany) and the 3 GW Xiluodo (China) showcase their scalability. Research continues into solid-state transformer integrations and AI-based predictive maintenance.

Mathematical Underpinnings of Early MMC Control

The fundamental voltage balancing equation for a submodule capacitor, derived from energy conservation principles, is:

$$ \frac{dV_{sm}}{dt} = \frac{i_{arm}}{C_{sm}} \cdot S $$

where Vsm is the submodule capacitor voltage, iarm the arm current, Csm the capacitance, and S the switching state (0 or 1). Early control systems relied on linearized approximations of this nonlinear relationship.

Evolution of MMC Submodule Count in HVDC Projects 2010 2014 2018 2022

1.3 Key Advantages Over Traditional Converters

Modular Multilevel Converters (MMCs) exhibit several superior characteristics compared to conventional two-level or three-level voltage source converters (VSCs). These advantages stem from their modular architecture, distributed energy storage, and advanced control strategies.

Higher Voltage Handling with Lower Harmonic Distortion

Traditional converters require series-connected semiconductor devices to handle high voltages, leading to complex voltage balancing and increased switching losses. MMCs inherently distribute voltage stress across multiple submodules (SMs), enabling operation at higher voltages without series-stacking. The output voltage waveform is synthesized from numerous small voltage steps, reducing harmonic content. The total harmonic distortion (THD) for an MMC with N submodules per arm is approximated by:

$$ THD \approx \frac{100\%}{2N \sqrt{3}} $$

For example, an MMC with 10 submodules per arm achieves a THD below 3%, whereas a two-level converter typically exceeds 30% without additional filters.

Reduced Switching Losses and Improved Efficiency

MMCs operate at near-fundamental frequency switching for most submodules, minimizing switching losses. Only a fraction of SMs switch at high frequency at any given time, distributing thermal stress. The total converter losses Ploss can be modeled as:

$$ P_{loss} = N \left( P_{cond} + \frac{f_{sw}}{N} E_{sw} \right) $$

where Pcond represents conduction losses, fsw is the effective switching frequency, and Esw is the energy loss per switching event. This results in typical efficiencies exceeding 99% for high-power applications.

Fault Tolerance and Redundancy

The modular design allows continued operation with failed submodules through redundant SMs. If k submodules fail in an arm with N + r SMs (where r is the redundancy factor), the converter maintains full functionality by bypassing failed units. The probability of system failure Pfail follows:

$$ P_{fail} = 1 - \sum_{i=0}^{r} \binom{N+r}{i} p^i (1-p)^{N+r-i} $$

where p is the individual submodule failure probability. This fault tolerance is critical for HVDC transmission and industrial drives.

Scalability and Flexible Voltage Ratings

MMCs achieve virtually any voltage rating by adding or removing submodules, unlike traditional converters that require complete redesign for different voltage classes. The output voltage Vout scales linearly with the number of active submodules Nactive:

$$ V_{out} = \frac{N_{active}}{2} V_{SM} $$

where VSM is the nominal voltage of each submodule. This scalability makes MMCs ideal for applications ranging from medium-voltage drives (3-10 kV) to ultra-high-voltage DC transmission (±800 kV).

Common-Mode Voltage Elimination

Traditional converters generate high common-mode voltages that induce bearing currents and electromagnetic interference. MMCs inherently balance the positive and negative arm voltages, eliminating common-mode voltage. The circulating current icirc in the phase leg cancels common-mode components:

$$ i_{circ} = \frac{i_{upper} + i_{lower}}{2} $$

This property significantly reduces motor insulation stress in drive applications and minimizes EMI in sensitive environments.

Grid-Friendly Behavior

MMCs provide inherent energy buffering through distributed capacitors, enabling ride-through capability during grid disturbances. The stored energy Etotal scales with the number of submodules:

$$ E_{total} = \frac{1}{2} C_{SM} V_{SM}^2 \times 6N $$

where CSM is the submodule capacitance. This energy reservoir allows MMCs to inject reactive power during voltage sags without external energy storage, exceeding grid code requirements for renewable energy plants.

MMC vs Traditional Converter Voltage Waveforms Comparison of voltage waveforms between Modular Multilevel Converters (stepped output) and traditional two-level converters (square-wave output), including harmonic spectra analysis. MMC vs Traditional Converter Voltage Waveforms MMC (N=10) THD: 3.2% 0 π 2π V Traditional Two-Level THD: 28.8% 0 π 2π V MMC Harmonic Spectrum Traditional Harmonic Spectrum 0 5 10 15 20 % 0 5 10 15 20 % Harmonic Order (Fundamental = 50Hz)
Diagram Description: A diagram would visually compare the voltage waveforms of MMCs (with stepped output) versus traditional converters (with square-wave output) to illustrate harmonic distortion differences.

1.3 Key Advantages Over Traditional Converters

Modular Multilevel Converters (MMCs) exhibit several superior characteristics compared to conventional two-level or three-level voltage source converters (VSCs). These advantages stem from their modular architecture, distributed energy storage, and advanced control strategies.

Higher Voltage Handling with Lower Harmonic Distortion

Traditional converters require series-connected semiconductor devices to handle high voltages, leading to complex voltage balancing and increased switching losses. MMCs inherently distribute voltage stress across multiple submodules (SMs), enabling operation at higher voltages without series-stacking. The output voltage waveform is synthesized from numerous small voltage steps, reducing harmonic content. The total harmonic distortion (THD) for an MMC with N submodules per arm is approximated by:

$$ THD \approx \frac{100\%}{2N \sqrt{3}} $$

For example, an MMC with 10 submodules per arm achieves a THD below 3%, whereas a two-level converter typically exceeds 30% without additional filters.

Reduced Switching Losses and Improved Efficiency

MMCs operate at near-fundamental frequency switching for most submodules, minimizing switching losses. Only a fraction of SMs switch at high frequency at any given time, distributing thermal stress. The total converter losses Ploss can be modeled as:

$$ P_{loss} = N \left( P_{cond} + \frac{f_{sw}}{N} E_{sw} \right) $$

where Pcond represents conduction losses, fsw is the effective switching frequency, and Esw is the energy loss per switching event. This results in typical efficiencies exceeding 99% for high-power applications.

Fault Tolerance and Redundancy

The modular design allows continued operation with failed submodules through redundant SMs. If k submodules fail in an arm with N + r SMs (where r is the redundancy factor), the converter maintains full functionality by bypassing failed units. The probability of system failure Pfail follows:

$$ P_{fail} = 1 - \sum_{i=0}^{r} \binom{N+r}{i} p^i (1-p)^{N+r-i} $$

where p is the individual submodule failure probability. This fault tolerance is critical for HVDC transmission and industrial drives.

Scalability and Flexible Voltage Ratings

MMCs achieve virtually any voltage rating by adding or removing submodules, unlike traditional converters that require complete redesign for different voltage classes. The output voltage Vout scales linearly with the number of active submodules Nactive:

$$ V_{out} = \frac{N_{active}}{2} V_{SM} $$

where VSM is the nominal voltage of each submodule. This scalability makes MMCs ideal for applications ranging from medium-voltage drives (3-10 kV) to ultra-high-voltage DC transmission (±800 kV).

Common-Mode Voltage Elimination

Traditional converters generate high common-mode voltages that induce bearing currents and electromagnetic interference. MMCs inherently balance the positive and negative arm voltages, eliminating common-mode voltage. The circulating current icirc in the phase leg cancels common-mode components:

$$ i_{circ} = \frac{i_{upper} + i_{lower}}{2} $$

This property significantly reduces motor insulation stress in drive applications and minimizes EMI in sensitive environments.

Grid-Friendly Behavior

MMCs provide inherent energy buffering through distributed capacitors, enabling ride-through capability during grid disturbances. The stored energy Etotal scales with the number of submodules:

$$ E_{total} = \frac{1}{2} C_{SM} V_{SM}^2 \times 6N $$

where CSM is the submodule capacitance. This energy reservoir allows MMCs to inject reactive power during voltage sags without external energy storage, exceeding grid code requirements for renewable energy plants.

MMC vs Traditional Converter Voltage Waveforms Comparison of voltage waveforms between Modular Multilevel Converters (stepped output) and traditional two-level converters (square-wave output), including harmonic spectra analysis. MMC vs Traditional Converter Voltage Waveforms MMC (N=10) THD: 3.2% 0 π 2π V Traditional Two-Level THD: 28.8% 0 π 2π V MMC Harmonic Spectrum Traditional Harmonic Spectrum 0 5 10 15 20 % 0 5 10 15 20 % Harmonic Order (Fundamental = 50Hz)
Diagram Description: A diagram would visually compare the voltage waveforms of MMCs (with stepped output) versus traditional converters (with square-wave output) to illustrate harmonic distortion differences.

2. Basic Submodule Structure and Functionality

2.1 Basic Submodule Structure and Functionality

The fundamental building block of a Modular Multilevel Converter (MMC) is the submodule (SM), which functions as a controllable voltage source. Each SM typically consists of a half-bridge or full-bridge inverter, a DC capacitor, and switching devices (IGBTs or MOSFETs with anti-parallel diodes). The topology determines the SM's voltage synthesis capability and fault tolerance.

Half-Bridge Submodule (HBSM)

The most widely used configuration is the half-bridge submodule, comprising two switches (S1 and S2) and a capacitor C. The output voltage VSM can be either VC (capacitor voltage) or 0, depending on the switching state:

$$ V_{SM} = \begin{cases} V_C & \text{if } S_1 \text{ is ON and } S_2 \text{ is OFF}, \\ 0 & \text{if } S_2 \text{ is ON and } S_1 \text{ is OFF}. \end{cases} $$

The capacitor voltage VC is regulated by controlling the duty cycle of the switches, ensuring energy balance in the MMC arm. The HBSM offers simplicity and low conduction losses but lacks fault blocking capability.

Full-Bridge Submodule (FBSM)

For higher flexibility, the full-bridge submodule employs four switches (S1–S4) and a capacitor. It can generate three output states: +VC, −VC, or 0:

$$ V_{SM} = \begin{cases} +V_C & \text{if } S_1 \text{ and } S_4 \text{ are ON}, \\ -V_C & \text{if } S_2 \text{ and } S_3 \text{ are ON}, \\ 0 & \text{if } S_1 \text{ and } S_2 \text{ or } S_3 \text{ and } S_4 \text{ are ON}. \end{cases} $$

FBSMs enable bidirectional current flow and DC fault blocking, making them suitable for HVDC applications. However, they incur higher conduction losses and costs due to additional switches.

Capacitor Voltage Balancing

Maintaining uniform capacitor voltages across SMs is critical for MMC performance. A sorting algorithm dynamically prioritizes SMs based on:

The energy dynamics of a single SM capacitor are governed by:

$$ \frac{d}{dt} \left( \frac{1}{2} C V_C^2 \right) = V_C \cdot i_{arm}, $$

where iarm is the arm current. Closed-loop control ensures VC tracks the reference voltage Vref.

Practical Considerations

Real-world implementations must account for:

HBSM FBSM
Half-Bridge vs. Full-Bridge Submodule Topologies Side-by-side comparison of Half-Bridge Submodule (HBSM) and Full-Bridge Submodule (FBSM) with labeled switches (S1-S4), capacitor (C), output terminals, and current paths. Half-Bridge vs. Full-Bridge Submodule Topologies Half-Bridge Submodule (HBSM) S1 S2 C V_SM 0 +V_C -V_C Full-Bridge Submodule (FBSM) S1 S2 S3 S4 C V_SM 0 +V_C -V_C
Diagram Description: The section describes the physical structure and switching states of half-bridge and full-bridge submodules, which are inherently visual concepts.

2.1 Basic Submodule Structure and Functionality

The fundamental building block of a Modular Multilevel Converter (MMC) is the submodule (SM), which functions as a controllable voltage source. Each SM typically consists of a half-bridge or full-bridge inverter, a DC capacitor, and switching devices (IGBTs or MOSFETs with anti-parallel diodes). The topology determines the SM's voltage synthesis capability and fault tolerance.

Half-Bridge Submodule (HBSM)

The most widely used configuration is the half-bridge submodule, comprising two switches (S1 and S2) and a capacitor C. The output voltage VSM can be either VC (capacitor voltage) or 0, depending on the switching state:

$$ V_{SM} = \begin{cases} V_C & \text{if } S_1 \text{ is ON and } S_2 \text{ is OFF}, \\ 0 & \text{if } S_2 \text{ is ON and } S_1 \text{ is OFF}. \end{cases} $$

The capacitor voltage VC is regulated by controlling the duty cycle of the switches, ensuring energy balance in the MMC arm. The HBSM offers simplicity and low conduction losses but lacks fault blocking capability.

Full-Bridge Submodule (FBSM)

For higher flexibility, the full-bridge submodule employs four switches (S1–S4) and a capacitor. It can generate three output states: +VC, −VC, or 0:

$$ V_{SM} = \begin{cases} +V_C & \text{if } S_1 \text{ and } S_4 \text{ are ON}, \\ -V_C & \text{if } S_2 \text{ and } S_3 \text{ are ON}, \\ 0 & \text{if } S_1 \text{ and } S_2 \text{ or } S_3 \text{ and } S_4 \text{ are ON}. \end{cases} $$

FBSMs enable bidirectional current flow and DC fault blocking, making them suitable for HVDC applications. However, they incur higher conduction losses and costs due to additional switches.

Capacitor Voltage Balancing

Maintaining uniform capacitor voltages across SMs is critical for MMC performance. A sorting algorithm dynamically prioritizes SMs based on:

The energy dynamics of a single SM capacitor are governed by:

$$ \frac{d}{dt} \left( \frac{1}{2} C V_C^2 \right) = V_C \cdot i_{arm}, $$

where iarm is the arm current. Closed-loop control ensures VC tracks the reference voltage Vref.

Practical Considerations

Real-world implementations must account for:

HBSM FBSM
Half-Bridge vs. Full-Bridge Submodule Topologies Side-by-side comparison of Half-Bridge Submodule (HBSM) and Full-Bridge Submodule (FBSM) with labeled switches (S1-S4), capacitor (C), output terminals, and current paths. Half-Bridge vs. Full-Bridge Submodule Topologies Half-Bridge Submodule (HBSM) S1 S2 C V_SM 0 +V_C -V_C Full-Bridge Submodule (FBSM) S1 S2 S3 S4 C V_SM 0 +V_C -V_C
Diagram Description: The section describes the physical structure and switching states of half-bridge and full-bridge submodules, which are inherently visual concepts.

Series and Parallel Configurations

Voltage and Current Distribution in Series-Connected Submodules

In a series configuration, submodules (SMs) are connected in a cascaded fashion to achieve higher voltage blocking capability. The total output voltage Vout is the sum of individual SM capacitor voltages:

$$ V_{out} = \sum_{k=1}^{N} v_{C_k} $$

where N is the number of series-connected SMs and vC_k is the voltage across the k-th capacitor. The current through all SMs remains identical in steady-state operation, given by:

$$ I_{arm} = \frac{P_{total}}{V_{out}} $$

where Ptotal is the total power processed by the converter arm. Voltage balancing algorithms are critical to maintain equal voltage distribution across SMs under dynamic load conditions.

Parallel Configurations for Current Sharing

Parallel configurations are employed to increase current-handling capacity. The total output current Iout divides among M parallel-connected arms:

$$ I_{out} = \sum_{j=1}^{M} I_{arm_j} $$

Each parallel arm must maintain identical impedance characteristics to ensure natural current sharing. Circulating currents between parallel paths can be minimized through:

Hybrid Series-Parallel Topologies

Practical MMC implementations often combine series and parallel connections. For an N×M matrix configuration (N series, M parallel):

$$ V_{block} = N \cdot V_{SM} $$ $$ I_{max} = M \cdot I_{SM} $$

where VSM and ISM represent individual submodule ratings. The modularity enables voltage and current scaling while maintaining:

Impedance Matching Considerations

The equivalent impedance Zeq of series-parallel configurations follows:

$$ Z_{eq} = \frac{N}{M} Z_{SM} $$

where ZSM is the submodule impedance. This relationship impacts:

Practical implementations in HVDC applications (e.g., 400kV/1.2GW systems) demonstrate configuration ratios up to N=200, M=4, with individual submodule voltages of 2kV.

MMC Series-Parallel Submodule Configurations Schematic diagram of Modular Multilevel Converter (MMC) submodule configurations, showing series, parallel, and hybrid connections with labeled voltages and currents. Series Configuration SM SM V_SM V_SM ΣV_out = N×V_SM I_arm = I_SM N series Parallel Configuration SM SM V_out = V_SM I_arm = M×I_SM Z_SM Z_SM M parallel Hybrid Configuration SM SM SM SM ΣV_out = N×V_SM I_arm = M×I_SM N×M Matrix
Diagram Description: The section describes complex series-parallel configurations and hybrid topologies that require visual representation of submodule connections and current/voltage distribution.

Series and Parallel Configurations

Voltage and Current Distribution in Series-Connected Submodules

In a series configuration, submodules (SMs) are connected in a cascaded fashion to achieve higher voltage blocking capability. The total output voltage Vout is the sum of individual SM capacitor voltages:

$$ V_{out} = \sum_{k=1}^{N} v_{C_k} $$

where N is the number of series-connected SMs and vC_k is the voltage across the k-th capacitor. The current through all SMs remains identical in steady-state operation, given by:

$$ I_{arm} = \frac{P_{total}}{V_{out}} $$

where Ptotal is the total power processed by the converter arm. Voltage balancing algorithms are critical to maintain equal voltage distribution across SMs under dynamic load conditions.

Parallel Configurations for Current Sharing

Parallel configurations are employed to increase current-handling capacity. The total output current Iout divides among M parallel-connected arms:

$$ I_{out} = \sum_{j=1}^{M} I_{arm_j} $$

Each parallel arm must maintain identical impedance characteristics to ensure natural current sharing. Circulating currents between parallel paths can be minimized through:

Hybrid Series-Parallel Topologies

Practical MMC implementations often combine series and parallel connections. For an N×M matrix configuration (N series, M parallel):

$$ V_{block} = N \cdot V_{SM} $$ $$ I_{max} = M \cdot I_{SM} $$

where VSM and ISM represent individual submodule ratings. The modularity enables voltage and current scaling while maintaining:

Impedance Matching Considerations

The equivalent impedance Zeq of series-parallel configurations follows:

$$ Z_{eq} = \frac{N}{M} Z_{SM} $$

where ZSM is the submodule impedance. This relationship impacts:

Practical implementations in HVDC applications (e.g., 400kV/1.2GW systems) demonstrate configuration ratios up to N=200, M=4, with individual submodule voltages of 2kV.

MMC Series-Parallel Submodule Configurations Schematic diagram of Modular Multilevel Converter (MMC) submodule configurations, showing series, parallel, and hybrid connections with labeled voltages and currents. Series Configuration SM SM V_SM V_SM ΣV_out = N×V_SM I_arm = I_SM N series Parallel Configuration SM SM V_out = V_SM I_arm = M×I_SM Z_SM Z_SM M parallel Hybrid Configuration SM SM SM SM ΣV_out = N×V_SM I_arm = M×I_SM N×M Matrix
Diagram Description: The section describes complex series-parallel configurations and hybrid topologies that require visual representation of submodule connections and current/voltage distribution.

2.3 Voltage Balancing Techniques

Fundamentals of Voltage Balancing in MMCs

Voltage balancing in Modular Multilevel Converters (MMCs) is critical to ensure stable operation and prevent overvoltage stress on submodule (SM) capacitors. The primary challenge arises from the fluctuating energy stored in each SM capacitor due to load variations and switching dynamics. Without active balancing, capacitor voltages diverge, leading to distorted output waveforms and potential device failure.

The energy variation in an SM capacitor can be expressed as:

$$ \Delta E_{SM} = \frac{1}{2}C_{SM} \left( V_{SM,max}^2 - V_{SM,min}^2 \right) $$

where CSM is the submodule capacitance, and VSM,max, VSM,min are the maximum and minimum allowable capacitor voltages, respectively.

Categories of Voltage Balancing Techniques

Voltage balancing methods for MMCs fall into two broad categories:

Sorting-Based Voltage Balancing

The sorting algorithm is the most widely implemented technique due to its simplicity and effectiveness. The steps are:

  1. Measure all SM capacitor voltages in an arm.
  2. Sort SMs in descending order of voltage when the arm current is positive (charging).
  3. Sort SMs in ascending order when the arm current is negative (discharging).
  4. Select the required number of SMs from the sorted list for insertion.

The sorting period must be fast enough to track voltage variations but not so frequent as to cause excessive computational load. A typical implementation uses a carrier-based PWM scheme with sorting executed at every PWM cycle.

Closed-Loop Balancing Techniques

Advanced balancing methods employ closed-loop control to achieve faster response and better disturbance rejection. The energy-based balancing controller is derived from the arm energy dynamics:

$$ \frac{dE_{arm}}{dt} = v_{arm} \cdot i_{arm} $$

where Earm is the total energy in an arm, varm is the arm voltage, and iarm is the arm current. The controller adjusts the insertion index to regulate the average capacitor voltage:

$$ n_{insert} = \frac{V_{arm}^*}{V_{SM,avg}} + \Delta n $$

Here, Varm* is the reference arm voltage, VSM,avg is the average SM voltage, and Δn is the correction term from the energy controller.

Model Predictive Control (MPC) Approach

MPC optimizes SM selection by predicting future capacitor voltages based on current measurements and system models. The cost function minimizes both voltage deviations and switching frequency:

$$ J = \sum_{k=1}^{N} \left( \alpha \| V_{SM}(k) - V_{ref} \|^2 + \beta \| \Delta S(k) \|^2 \right) $$

where α and β are weighting factors, VSM(k) are predicted voltages, and ΔS(k) represents switching transitions.

Practical Implementation Considerations

Real-world MMC systems must address several challenges in voltage balancing:

Modern MMCs often combine sorting with closed-loop methods - using sorting for coarse balancing and feedback control for fine adjustments. This hybrid approach achieves both robustness and precision.

MMC Voltage Balancing Techniques Comparison A comparison diagram of sorting-based and closed-loop voltage balancing techniques for Modular Multilevel Converters (MMCs), showing submodule capacitor voltages, arm currents, and control logic. MMC Voltage Balancing Techniques Comparison Sorting-Based Method Submodule Voltage Ranking 1. V_SM,max 2. V_SM,avg+Δ N. V_SM,min i_arm (charging/discharging) Current-Dependent Selection PWM Signals Closed-Loop Control V_SM Measurements Controller Δn correction term V_arm^* Reference Insertion Index Calculation PWM Signals Solid: Active Paths | Dashed: Auxiliary Elements
Diagram Description: The section describes sorting-based voltage balancing and closed-loop control methods, which involve dynamic relationships between SM capacitor voltages, arm currents, and switching patterns that are best visualized.

2.3 Voltage Balancing Techniques

Fundamentals of Voltage Balancing in MMCs

Voltage balancing in Modular Multilevel Converters (MMCs) is critical to ensure stable operation and prevent overvoltage stress on submodule (SM) capacitors. The primary challenge arises from the fluctuating energy stored in each SM capacitor due to load variations and switching dynamics. Without active balancing, capacitor voltages diverge, leading to distorted output waveforms and potential device failure.

The energy variation in an SM capacitor can be expressed as:

$$ \Delta E_{SM} = \frac{1}{2}C_{SM} \left( V_{SM,max}^2 - V_{SM,min}^2 \right) $$

where CSM is the submodule capacitance, and VSM,max, VSM,min are the maximum and minimum allowable capacitor voltages, respectively.

Categories of Voltage Balancing Techniques

Voltage balancing methods for MMCs fall into two broad categories:

Sorting-Based Voltage Balancing

The sorting algorithm is the most widely implemented technique due to its simplicity and effectiveness. The steps are:

  1. Measure all SM capacitor voltages in an arm.
  2. Sort SMs in descending order of voltage when the arm current is positive (charging).
  3. Sort SMs in ascending order when the arm current is negative (discharging).
  4. Select the required number of SMs from the sorted list for insertion.

The sorting period must be fast enough to track voltage variations but not so frequent as to cause excessive computational load. A typical implementation uses a carrier-based PWM scheme with sorting executed at every PWM cycle.

Closed-Loop Balancing Techniques

Advanced balancing methods employ closed-loop control to achieve faster response and better disturbance rejection. The energy-based balancing controller is derived from the arm energy dynamics:

$$ \frac{dE_{arm}}{dt} = v_{arm} \cdot i_{arm} $$

where Earm is the total energy in an arm, varm is the arm voltage, and iarm is the arm current. The controller adjusts the insertion index to regulate the average capacitor voltage:

$$ n_{insert} = \frac{V_{arm}^*}{V_{SM,avg}} + \Delta n $$

Here, Varm* is the reference arm voltage, VSM,avg is the average SM voltage, and Δn is the correction term from the energy controller.

Model Predictive Control (MPC) Approach

MPC optimizes SM selection by predicting future capacitor voltages based on current measurements and system models. The cost function minimizes both voltage deviations and switching frequency:

$$ J = \sum_{k=1}^{N} \left( \alpha \| V_{SM}(k) - V_{ref} \|^2 + \beta \| \Delta S(k) \|^2 \right) $$

where α and β are weighting factors, VSM(k) are predicted voltages, and ΔS(k) represents switching transitions.

Practical Implementation Considerations

Real-world MMC systems must address several challenges in voltage balancing:

Modern MMCs often combine sorting with closed-loop methods - using sorting for coarse balancing and feedback control for fine adjustments. This hybrid approach achieves both robustness and precision.

MMC Voltage Balancing Techniques Comparison A comparison diagram of sorting-based and closed-loop voltage balancing techniques for Modular Multilevel Converters (MMCs), showing submodule capacitor voltages, arm currents, and control logic. MMC Voltage Balancing Techniques Comparison Sorting-Based Method Submodule Voltage Ranking 1. V_SM,max 2. V_SM,avg+Δ N. V_SM,min i_arm (charging/discharging) Current-Dependent Selection PWM Signals Closed-Loop Control V_SM Measurements Controller Δn correction term V_arm^* Reference Insertion Index Calculation PWM Signals Solid: Active Paths | Dashed: Auxiliary Elements
Diagram Description: The section describes sorting-based voltage balancing and closed-loop control methods, which involve dynamic relationships between SM capacitor voltages, arm currents, and switching patterns that are best visualized.

3. Modulation Techniques

3.1 Modulation Techniques

Modular Multilevel Converters (MMCs) rely on sophisticated modulation strategies to achieve high-quality voltage synthesis, capacitor voltage balancing, and harmonic suppression. The choice of modulation technique directly impacts efficiency, waveform fidelity, and dynamic response. This section examines the most prevalent methods, their mathematical foundations, and implementation trade-offs.

Pulse-Width Modulation (PWM) in MMCs

PWM techniques for MMCs must account for the distributed nature of submodule (SM) capacitors. Carrier-based PWM (CB-PWM) employs phase-shifted or level-shifted carriers to distribute switching events evenly across SMs. For a converter with N SMs per arm, the phase-shifted carrier (PSC-PWM) approach assigns each SM a carrier waveform with a phase offset of:

$$ \Delta heta = \frac{360^\circ}{N} $$

This ensures natural voltage balancing under steady-state conditions. The modulation index m determines the output voltage amplitude:

$$ V_{out} = m \cdot \frac{V_{dc}}{2} $$

where Vdc is the total DC-link voltage. PSC-PWM reduces effective switching frequency at the device level while maintaining high equivalent frequency at the output.

Nearest-Level Modulation (NLM)

NLM approximates the reference waveform by selecting the nearest available voltage level, minimizing switching losses in high-voltage applications. For a reference voltage vref, the output level k is determined by:

$$ k = \text{round}\left(\frac{v_{ref}}{V_{SM}}\right) $$

where VSM is the nominal submodule capacitor voltage. NLM introduces quantization error proportional to the reciprocal of the number of levels. Dynamic voltage balancing algorithms must supplement NLM to maintain SM capacitor equilibrium.

Space Vector Modulation (SVM) for MMCs

SVM extends to MMCs by treating the converter as a multi-dimensional switching system. The space vector diagram for an N-level MMC contains N3 switching states. The dwell times for adjacent vectors Vk and Vk+1 are calculated via:

$$ T_k = T_s \cdot \frac{\sin\left(\frac{\pi}{3} - heta_{ref}\right)}{\sin\left(\frac{\pi}{3}\right)} $$ $$ T_{k+1} = T_s \cdot \frac{\sin( heta_{ref})}{\sin\left(\frac{\pi}{3}\right)} $$

where Ts is the switching period and θref is the reference vector angle. SVM provides superior DC-link utilization compared to sinusoidal PWM but requires complex computation for vector selection in high-level converters.

Sorting Algorithms for Voltage Balancing

All modulation schemes require supplemental capacitor voltage control. The bubble-sort algorithm is commonly implemented in real-time controllers to prioritize switching of SMs with:

This sorting occurs at every switching interval, typically synchronized with the modulation cycle. Advanced variants incorporate:

Hybrid Modulation Strategies

Recent developments combine the advantages of multiple techniques:

These methods demonstrate 10-15% efficiency improvements in prototype MMC installations for HVDC applications, though with increased controller complexity.

MMC Modulation Techniques Comparison Comparison of three MMC modulation techniques: Phase-Shifted PWM carriers (left), Nearest Level Modulation steps (center), and Space Vector Modulation sectors (right). PSC-PWM Δθ = 120° V_out NLM V_SM = V_dc/N (N = number of levels) SVM V_k V_k+1 θ_ref T_k/T_s, T_k+1/T_s (dwell times)
Diagram Description: The section covers multiple modulation techniques with mathematical relationships between carrier waveforms, voltage levels, and vector transformations that are inherently spatial.

3.1 Modulation Techniques

Modular Multilevel Converters (MMCs) rely on sophisticated modulation strategies to achieve high-quality voltage synthesis, capacitor voltage balancing, and harmonic suppression. The choice of modulation technique directly impacts efficiency, waveform fidelity, and dynamic response. This section examines the most prevalent methods, their mathematical foundations, and implementation trade-offs.

Pulse-Width Modulation (PWM) in MMCs

PWM techniques for MMCs must account for the distributed nature of submodule (SM) capacitors. Carrier-based PWM (CB-PWM) employs phase-shifted or level-shifted carriers to distribute switching events evenly across SMs. For a converter with N SMs per arm, the phase-shifted carrier (PSC-PWM) approach assigns each SM a carrier waveform with a phase offset of:

$$ \Delta heta = \frac{360^\circ}{N} $$

This ensures natural voltage balancing under steady-state conditions. The modulation index m determines the output voltage amplitude:

$$ V_{out} = m \cdot \frac{V_{dc}}{2} $$

where Vdc is the total DC-link voltage. PSC-PWM reduces effective switching frequency at the device level while maintaining high equivalent frequency at the output.

Nearest-Level Modulation (NLM)

NLM approximates the reference waveform by selecting the nearest available voltage level, minimizing switching losses in high-voltage applications. For a reference voltage vref, the output level k is determined by:

$$ k = \text{round}\left(\frac{v_{ref}}{V_{SM}}\right) $$

where VSM is the nominal submodule capacitor voltage. NLM introduces quantization error proportional to the reciprocal of the number of levels. Dynamic voltage balancing algorithms must supplement NLM to maintain SM capacitor equilibrium.

Space Vector Modulation (SVM) for MMCs

SVM extends to MMCs by treating the converter as a multi-dimensional switching system. The space vector diagram for an N-level MMC contains N3 switching states. The dwell times for adjacent vectors Vk and Vk+1 are calculated via:

$$ T_k = T_s \cdot \frac{\sin\left(\frac{\pi}{3} - heta_{ref}\right)}{\sin\left(\frac{\pi}{3}\right)} $$ $$ T_{k+1} = T_s \cdot \frac{\sin( heta_{ref})}{\sin\left(\frac{\pi}{3}\right)} $$

where Ts is the switching period and θref is the reference vector angle. SVM provides superior DC-link utilization compared to sinusoidal PWM but requires complex computation for vector selection in high-level converters.

Sorting Algorithms for Voltage Balancing

All modulation schemes require supplemental capacitor voltage control. The bubble-sort algorithm is commonly implemented in real-time controllers to prioritize switching of SMs with:

This sorting occurs at every switching interval, typically synchronized with the modulation cycle. Advanced variants incorporate:

Hybrid Modulation Strategies

Recent developments combine the advantages of multiple techniques:

These methods demonstrate 10-15% efficiency improvements in prototype MMC installations for HVDC applications, though with increased controller complexity.

MMC Modulation Techniques Comparison Comparison of three MMC modulation techniques: Phase-Shifted PWM carriers (left), Nearest Level Modulation steps (center), and Space Vector Modulation sectors (right). PSC-PWM Δθ = 120° V_out NLM V_SM = V_dc/N (N = number of levels) SVM V_k V_k+1 θ_ref T_k/T_s, T_k+1/T_s (dwell times)
Diagram Description: The section covers multiple modulation techniques with mathematical relationships between carrier waveforms, voltage levels, and vector transformations that are inherently spatial.

3.2 Circulating Current Control

In Modular Multilevel Converters (MMCs), circulating currents are inherent phenomena caused by voltage imbalances between the upper and lower arms of each phase leg. These currents do not contribute to the output power but increase losses and thermal stress on the submodules. Effective control of circulating currents is essential for improving efficiency and ensuring stable operation.

Mathematical Modeling of Circulating Currents

The circulating current (icirc) in an MMC can be derived from the differential voltage between the upper and lower arm voltages. Considering a three-phase MMC, the dynamics of the circulating current in phase j (where j ∈ {a, b, c}) are described by:

$$ v_{uj} - v_{lj} = L_{arm} \frac{di_{circ,j}}{dt} + R_{arm} i_{circ,j} $$

where:

The circulating current typically contains a DC component and even-order harmonics (primarily the second harmonic) due to the interaction between the phase legs and the DC bus.

Control Strategies

Several methods exist to suppress circulating currents, each with distinct advantages:

1. Proportional-Resonant (PR) Control

A PR controller tuned to the second harmonic (2ω) can effectively eliminate the dominant harmonic component. The transfer function of the PR controller is:

$$ G_{PR}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$

where:

2. Feedforward Compensation

Feedforward techniques inject a compensating voltage to cancel the circulating current. The compensating voltage is derived from the measured DC bus voltage and modulation index:

$$ v_{comp,j} = \frac{V_{dc}}{2} \left(1 - m_j \sin(\omega t + \phi_j)\right) $$

where mj is the modulation index and ϕj is the phase angle.

3. Sliding Mode Control (SMC)

SMC provides robust performance under parameter variations. The sliding surface for circulating current control is defined as:

$$ S = i_{circ,j}^* - i_{circ,j} $$

where icirc,j* is the reference circulating current (ideally zero). The control law ensures convergence to the sliding surface.

Practical Implementation Considerations

In real-world MMC systems, the following factors must be addressed:

Case Study: HVDC Applications

In High-Voltage Direct Current (HVDC) transmission, MMCs with circulating current control achieve total harmonic distortion (THD) below 1%. A field study on a 320 kV MMC-HVDC link demonstrated a 15% reduction in losses after implementing a PR-based circulating current controller.

MMC Circulating Current Components and Control A diagram illustrating the components and control of circulating currents in Modular Multilevel Converters (MMCs), including arm voltage differentials, current waveforms, and control blocks. Arm Voltage Differential v_uj v_lj Δv_j Circulating Current (i_circ,j) Time Current DC + 2ω Component Control System G_PR(s) v_comp,j +
Diagram Description: The section involves voltage imbalances between upper/lower arms and harmonic components in circulating currents, which are inherently visual concepts.

3.2 Circulating Current Control

In Modular Multilevel Converters (MMCs), circulating currents are inherent phenomena caused by voltage imbalances between the upper and lower arms of each phase leg. These currents do not contribute to the output power but increase losses and thermal stress on the submodules. Effective control of circulating currents is essential for improving efficiency and ensuring stable operation.

Mathematical Modeling of Circulating Currents

The circulating current (icirc) in an MMC can be derived from the differential voltage between the upper and lower arm voltages. Considering a three-phase MMC, the dynamics of the circulating current in phase j (where j ∈ {a, b, c}) are described by:

$$ v_{uj} - v_{lj} = L_{arm} \frac{di_{circ,j}}{dt} + R_{arm} i_{circ,j} $$

where:

The circulating current typically contains a DC component and even-order harmonics (primarily the second harmonic) due to the interaction between the phase legs and the DC bus.

Control Strategies

Several methods exist to suppress circulating currents, each with distinct advantages:

1. Proportional-Resonant (PR) Control

A PR controller tuned to the second harmonic (2ω) can effectively eliminate the dominant harmonic component. The transfer function of the PR controller is:

$$ G_{PR}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$

where:

2. Feedforward Compensation

Feedforward techniques inject a compensating voltage to cancel the circulating current. The compensating voltage is derived from the measured DC bus voltage and modulation index:

$$ v_{comp,j} = \frac{V_{dc}}{2} \left(1 - m_j \sin(\omega t + \phi_j)\right) $$

where mj is the modulation index and ϕj is the phase angle.

3. Sliding Mode Control (SMC)

SMC provides robust performance under parameter variations. The sliding surface for circulating current control is defined as:

$$ S = i_{circ,j}^* - i_{circ,j} $$

where icirc,j* is the reference circulating current (ideally zero). The control law ensures convergence to the sliding surface.

Practical Implementation Considerations

In real-world MMC systems, the following factors must be addressed:

Case Study: HVDC Applications

In High-Voltage Direct Current (HVDC) transmission, MMCs with circulating current control achieve total harmonic distortion (THD) below 1%. A field study on a 320 kV MMC-HVDC link demonstrated a 15% reduction in losses after implementing a PR-based circulating current controller.

MMC Circulating Current Components and Control A diagram illustrating the components and control of circulating currents in Modular Multilevel Converters (MMCs), including arm voltage differentials, current waveforms, and control blocks. Arm Voltage Differential v_uj v_lj Δv_j Circulating Current (i_circ,j) Time Current DC + 2ω Component Control System G_PR(s) v_comp,j +
Diagram Description: The section involves voltage imbalances between upper/lower arms and harmonic components in circulating currents, which are inherently visual concepts.

3.3 Fault Detection and Mitigation

Fault detection and mitigation in Modular Multilevel Converters (MMCs) are critical for ensuring system reliability, particularly in high-voltage direct current (HVDC) transmission and flexible AC transmission systems (FACTS). MMCs are susceptible to submodule (SM) faults, arm imbalances, and DC-side short circuits, which require rapid identification and corrective action to prevent cascading failures.

Fault Types and Detection Methods

Common fault scenarios in MMCs include:

Detection methods leverage real-time measurements of capacitor voltages, arm currents, and circulating currents. A widely adopted approach is the voltage deviation method, where the measured SM capacitor voltage \( V_{C} \) is compared to its reference value \( V_{C,ref} \):

$$ \Delta V_C = |V_C - V_{C,ref}| $$

A fault is flagged if \( \Delta V_C \) exceeds a predefined threshold \( \epsilon \). For arm current monitoring, the differential current \( I_{diff} \) between upper and lower arms is analyzed:

$$ I_{diff} = \frac{I_{upper} - I_{lower}}{2} $$

Abnormal \( I_{diff} \) indicates SM failures or control instability.

Mitigation Strategies

Upon fault detection, MMCs employ redundant SMs or bypass strategies to maintain operation. The bypass thyristor method disconnects faulty SMs while redistributing energy to healthy modules. The post-fault arm voltage \( V_{arm} \) is adjusted as:

$$ V_{arm} = N_{active} \cdot V_C $$

where \( N_{active} \) is the number of operational SMs per arm. For DC-side faults, blocking mode forces all IGBTs off, allowing freewheeling diodes to clamp overvoltages.

Advanced Techniques

Recent research integrates machine learning for predictive fault detection. Neural networks trained on historical fault data can identify anomalies before threshold-based methods. Hardware solutions like active neutral-point clamped (ANPC) SMs provide additional fault tolerance by enabling bidirectional blocking.

MMC Fault Detection and Mitigation Voltage Monitoring Current Analysis Bypass Control
MMC Fault Detection and Mitigation Workflow Block diagram illustrating the fault detection and mitigation workflow in Modular Multilevel Converters (MMCs), including submodule voltage monitoring, arm current differential analysis, bypass thyristor activation, and blocking mode. Submodule Voltage Monitoring ΔV_C threshold Arm Current Differential I_diff analysis Voltage Fault? Current Fault? Bypass Thyristor Activation Adjust N_active SMs Blocking Mode Diodes engaged Fault Detection and Mitigation Workflow Parallel monitoring paths converge on mitigation actions
Diagram Description: The section describes complex fault detection workflows and mitigation strategies involving multiple interacting components (SM failures, arm currents, bypass control) that benefit from visual representation of their relationships.

3.3 Fault Detection and Mitigation

Fault detection and mitigation in Modular Multilevel Converters (MMCs) are critical for ensuring system reliability, particularly in high-voltage direct current (HVDC) transmission and flexible AC transmission systems (FACTS). MMCs are susceptible to submodule (SM) faults, arm imbalances, and DC-side short circuits, which require rapid identification and corrective action to prevent cascading failures.

Fault Types and Detection Methods

Common fault scenarios in MMCs include:

Detection methods leverage real-time measurements of capacitor voltages, arm currents, and circulating currents. A widely adopted approach is the voltage deviation method, where the measured SM capacitor voltage \( V_{C} \) is compared to its reference value \( V_{C,ref} \):

$$ \Delta V_C = |V_C - V_{C,ref}| $$

A fault is flagged if \( \Delta V_C \) exceeds a predefined threshold \( \epsilon \). For arm current monitoring, the differential current \( I_{diff} \) between upper and lower arms is analyzed:

$$ I_{diff} = \frac{I_{upper} - I_{lower}}{2} $$

Abnormal \( I_{diff} \) indicates SM failures or control instability.

Mitigation Strategies

Upon fault detection, MMCs employ redundant SMs or bypass strategies to maintain operation. The bypass thyristor method disconnects faulty SMs while redistributing energy to healthy modules. The post-fault arm voltage \( V_{arm} \) is adjusted as:

$$ V_{arm} = N_{active} \cdot V_C $$

where \( N_{active} \) is the number of operational SMs per arm. For DC-side faults, blocking mode forces all IGBTs off, allowing freewheeling diodes to clamp overvoltages.

Advanced Techniques

Recent research integrates machine learning for predictive fault detection. Neural networks trained on historical fault data can identify anomalies before threshold-based methods. Hardware solutions like active neutral-point clamped (ANPC) SMs provide additional fault tolerance by enabling bidirectional blocking.

MMC Fault Detection and Mitigation Voltage Monitoring Current Analysis Bypass Control
MMC Fault Detection and Mitigation Workflow Block diagram illustrating the fault detection and mitigation workflow in Modular Multilevel Converters (MMCs), including submodule voltage monitoring, arm current differential analysis, bypass thyristor activation, and blocking mode. Submodule Voltage Monitoring ΔV_C threshold Arm Current Differential I_diff analysis Voltage Fault? Current Fault? Bypass Thyristor Activation Adjust N_active SMs Blocking Mode Diodes engaged Fault Detection and Mitigation Workflow Parallel monitoring paths converge on mitigation actions
Diagram Description: The section describes complex fault detection workflows and mitigation strategies involving multiple interacting components (SM failures, arm currents, bypass control) that benefit from visual representation of their relationships.

4. High-Voltage Direct Current (HVDC) Transmission

4.1 High-Voltage Direct Current (HVDC) Transmission

High-Voltage Direct Current (HVDC) transmission systems leverage Modular Multilevel Converters (MMCs) for efficient long-distance power transfer with minimal losses. Unlike traditional Line-Commutated Converters (LCCs), MMCs offer superior harmonic performance, black-start capability, and bidirectional power flow without requiring external commutation voltage.

Operating Principles of MMCs in HVDC

The MMC topology consists of multiple submodules (SMs) connected in series, each containing a half-bridge or full-bridge configuration with insulated-gate bipolar transistors (IGBTs) and capacitors. The voltage balancing across SMs is achieved through a cascaded control structure:

$$ V_{dc} = N \cdot V_{SM} $$

where Vdc is the total DC-link voltage, N is the number of submodules per arm, and VSM is the individual submodule capacitor voltage. The arm currents are regulated using:

$$ \frac{di_{arm}}{dt} = \frac{V_{dc} - 2V_{SM}}{L_{arm}} $$

where Larm represents the arm inductance.

Control Strategies for HVDC Applications

MMCs employ hierarchical control:

The circulating current suppression controller (CCSC) mitigates internal energy oscillations using:

$$ v_{diff} = -k_p \cdot i_{circ} - k_i \int i_{circ} \, dt $$

Advantages Over LCC-HVDC

MMC-based HVDC systems provide:

Real-World Implementations

The DolWin3 project in the North Sea uses MMC technology to transmit 900 MW at ±320 kV DC over 160 km, with total losses below 1%. China's Zhangbei HVDC grid employs hybrid MMCs with full-bridge submodules for flexible power reversal and DC fault clearance.

MMC Station AC Grid HVDC Line
MMC-HVDC System Topology Schematic diagram of a Modular Multilevel Converter (MMC) HVDC system, showing AC grid connection, MMC station with submodules, arm inductors, and HVDC transmission line. AC Grid MMC Station Upper Arm Lower Arm L_arm SM SM IGBTs Capacitors V_dc HVDC Line AC DC
Diagram Description: The diagram would show the physical topology of an MMC-HVDC system, including submodule arrangement, arm connections, and grid interfaces.

4.1 High-Voltage Direct Current (HVDC) Transmission

High-Voltage Direct Current (HVDC) transmission systems leverage Modular Multilevel Converters (MMCs) for efficient long-distance power transfer with minimal losses. Unlike traditional Line-Commutated Converters (LCCs), MMCs offer superior harmonic performance, black-start capability, and bidirectional power flow without requiring external commutation voltage.

Operating Principles of MMCs in HVDC

The MMC topology consists of multiple submodules (SMs) connected in series, each containing a half-bridge or full-bridge configuration with insulated-gate bipolar transistors (IGBTs) and capacitors. The voltage balancing across SMs is achieved through a cascaded control structure:

$$ V_{dc} = N \cdot V_{SM} $$

where Vdc is the total DC-link voltage, N is the number of submodules per arm, and VSM is the individual submodule capacitor voltage. The arm currents are regulated using:

$$ \frac{di_{arm}}{dt} = \frac{V_{dc} - 2V_{SM}}{L_{arm}} $$

where Larm represents the arm inductance.

Control Strategies for HVDC Applications

MMCs employ hierarchical control:

The circulating current suppression controller (CCSC) mitigates internal energy oscillations using:

$$ v_{diff} = -k_p \cdot i_{circ} - k_i \int i_{circ} \, dt $$

Advantages Over LCC-HVDC

MMC-based HVDC systems provide:

Real-World Implementations

The DolWin3 project in the North Sea uses MMC technology to transmit 900 MW at ±320 kV DC over 160 km, with total losses below 1%. China's Zhangbei HVDC grid employs hybrid MMCs with full-bridge submodules for flexible power reversal and DC fault clearance.

MMC Station AC Grid HVDC Line
MMC-HVDC System Topology Schematic diagram of a Modular Multilevel Converter (MMC) HVDC system, showing AC grid connection, MMC station with submodules, arm inductors, and HVDC transmission line. AC Grid MMC Station Upper Arm Lower Arm L_arm SM SM IGBTs Capacitors V_dc HVDC Line AC DC
Diagram Description: The diagram would show the physical topology of an MMC-HVDC system, including submodule arrangement, arm connections, and grid interfaces.

4.2 Renewable Energy Integration

Grid Integration Challenges

Renewable energy sources such as wind and solar exhibit inherent intermittency, leading to voltage and frequency fluctuations in power grids. Modular Multilevel Converters (MMCs) address these challenges by providing:

MMC Control Strategies for Renewables

The energy balancing dynamics of an MMC with N submodules per arm can be modeled using capacitor voltage dynamics:

$$ \frac{dv_{c,k}}{dt} = \frac{i_{\text{arm}}}{C_{\text{sm}}} (s_k - \langle s \rangle) $$

where vc,k is the k-th submodule capacitor voltage, iarm the arm current, Csm the submodule capacitance, and sk the switching function. The circulating current icirc is minimized through:

$$ i_{\text{circ}} = \frac{1}{2}(i_{u} + i_{l}) - \frac{i_{\text{dc}}}{3} $$

where iu and il are upper/lower arm currents, and idc is the DC-link current.

Case Study: Offshore Wind Farms

MMCs dominate high-voltage DC (HVDC) transmission for offshore wind due to:

The German DolWin3 project exemplifies this, using MMCs to transmit 900 MW over 160 km with 97% efficiency.

Power Quality Enhancement

MMCs suppress characteristic harmonics (e.g., 6k±1 orders) through:

$$ \text{THD}_v = \frac{\sqrt{\sum_{h=2}^{\infty} V_h^2}}{V_1} \times 100\% $$

where Vh is the harmonic voltage magnitude. Experimental data from the NREL 1.5 MW solar plant shows THD reduction from 8.2% to 2.1% using MMCs.

Submodule Redundancy for Reliability

The reliability R(t) of an MMC with r redundant submodules follows:

$$ R(t) = \sum_{k=0}^{r} \binom{N+r}{k} e^{-\lambda kt} (1 - e^{-\lambda t})^{N+r-k} $$

where λ is the submodule failure rate. This enables 99.98% availability in the 2 GW North Sea Link interconnector.

MMC Arm Structure and Current Dynamics Schematic diagram of Modular Multilevel Converter (MMC) arm structure showing upper and lower arms with submodules, current paths (i_u, i_l, i_dc), and capacitor voltage dynamics. V_dc i_u Upper Arm N Submodules SM1 SM2 SMN Lower Arm N Submodules SM1 SM2 SMN i_l i_circ i_dc v_c1 v_c2 v_cN s_k ⟨s⟩ Legend Submodule (SM) i_arm i_circ v_c,k N submodules
Diagram Description: The section includes complex mathematical models of capacitor voltage dynamics and circulating current minimization, which would benefit from a visual representation of the MMC arm structure and current flow.

4.3 Industrial Motor Drives

Modular Multilevel Converters (MMCs) have emerged as a dominant topology for high-power industrial motor drives due to their superior voltage scalability, fault tolerance, and harmonic performance. Unlike conventional two-level or three-level converters, MMCs synthesize a near-sinusoidal output voltage by stacking multiple submodule (SM) capacitors, enabling operation at medium and high voltages without bulky transformers.

Operating Principle in Motor Drive Applications

The MMC's phase-leg consists of N series-connected submodules per arm, each capable of generating either +VSM or 0 at its terminals. For a motor drive application, the output voltage vout(t) is synthesized by dynamically inserting or bypassing SMs based on modulation strategies such as:

$$ v_{out}(t) = \frac{N_{inserted}}{N} \cdot V_{dc} \cdot \sin(\omega t + \phi) $$

where Ninserted is the number of active submodules, Vdc is the total DC-link voltage, and ϕ is the phase angle.

Circulating Current Control

A critical challenge in MMC-based motor drives is the suppression of arm-to-arm circulating currents, which do not contribute to output power but increase losses. The circulating current icirc in phase j can be expressed as:

$$ i_{circ,j} = \frac{i_{upper,j} + i_{lower,j}}{2} - \frac{i_{load,j}}{3} $$

where iupper,j and ilower,j are the upper and lower arm currents, respectively. Proportional-Resonant (PR) or repetitive controllers are typically employed to mitigate these currents at twice the output frequency.

Capacitor Voltage Balancing

Submodule capacitor voltage imbalance degrades output waveform quality and increases semiconductor stress. Sorting-based algorithms or model-predictive control (MPC) techniques dynamically adjust SM insertion order to maintain voltage equilibrium. The energy variation ΔW in a submodule capacitor C is given by:

$$ \Delta W = \frac{1}{2}C \left( V_{SM,max}^2 - V_{SM,min}^2 \right) $$

Modern implementations achieve balancing within 1% tolerance even under transient motor loads.

Practical Implementation Considerations

Industrial MMC motor drives require:

Field data from 6kV/5MW compressor drives show MMCs reducing THD to <2% compared to 8-12% in conventional MV drives, while achieving 98.5% efficiency across the speed range.

Comparison with Alternative Topologies

Topology Voltage Rating Efficiency THD
2-Level VSI ≤3.3kV 96-97% 8-15%
3-Level NPC ≤6.6kV 97-98% 5-8%
MMC ≥6.6kV 98-99% <3%

The modularity of MMCs allows direct scaling to 10kV+ applications where other topologies require complex series connections or multi-winding transformers.

MMC Phase-Leg Structure for Motor Drives Schematic of Modular Multilevel Converter (MMC) phase-leg structure with upper and lower arms, submodules, DC-link, and current flow paths. DC-Link Upper Arm Lower Arm SM SM SM SM Output i_circ i_upper i_lower i_load V_SM V_SM V_SM V_SM N Inserted SMs N Inserted SMs
Diagram Description: The diagram would show the MMC's phase-leg structure with submodules, illustrating how voltage synthesis and circulating currents occur spatially.

5. Thermal Management Issues

5.1 Thermal Management Issues

Thermal Challenges in MMCs

Modular Multilevel Converters (MMCs) are subject to significant thermal stresses due to high power density, switching losses, and conduction losses. The distributed nature of submodules (SMs) complicates heat dissipation, leading to localized hotspots that degrade semiconductor reliability. Key contributors to thermal stress include:

Mathematical Modeling of Power Losses

The total power loss in an MMC submodule can be decomposed into switching and conduction components. For an IGBT/diode pair, the average power loss per switching cycle is:

$$ P_{total} = P_{sw} + P_{cond} $$

Switching losses (Psw) are approximated as:

$$ P_{sw} = \frac{1}{T_s} \left( E_{on} + E_{off} \right) \cdot f_{sw} $$

where Eon and Eoff are turn-on/off energies, Ts is the switching period, and fsw is the switching frequency. Conduction losses (Pcond) for an IGBT and diode are:

$$ P_{cond} = V_{CE} \cdot I_{avg} + R_{CE} \cdot I_{rms}^2 + V_F \cdot I_{F,avg} + R_F \cdot I_{F,rms}^2 $$

Thermal Resistance Networks

Heat flow in an MMC submodule is modeled using a Foster or Cauer thermal network. The junction-to-case thermal impedance (Zth,jc) for a semiconductor device is:

$$ Z_{th,jc}(t) = \sum_{i=1}^n R_i \left( 1 - e^{-t/\tau_i} \right) $$

where Ri and τi are thermal resistances and time constants. The steady-state junction temperature (Tj) is derived from:

$$ T_j = T_a + P_{total} \cdot R_{th,ja} $$

Cooling Strategies

Effective thermal management in MMCs requires:

Case Study: HVDC Applications

In a 1.2 kV/600 A MMC for HVDC, thermal imaging revealed a 15°C gradient across SMs under unbalanced loading. Implementing 3D-printed microchannel coolers reduced the gradient to 3°C, extending lifetime by 2.8×.

5.2 Scalability and Cost Considerations

Scalability in MMC Design

The modularity of MMCs inherently supports scalability, allowing the system to be expanded by adding or removing submodules (SMs) as needed. The number of SMs per arm (N) directly impacts the output voltage resolution and harmonic performance. For a given DC-link voltage Vdc, the SM capacitor voltage (vc) is determined by:

$$ v_c = \frac{V_{dc}}{N} $$

Increasing N improves waveform quality but also raises complexity and cost. Practical implementations balance these factors—high-voltage applications (e.g., HVDC) may use hundreds of SMs per arm, while medium-voltage drives might employ fewer than 20.

Cost Drivers in MMC Systems

The primary cost components include:

Trade-offs Between Scalability and Cost

Optimizing an MMC involves minimizing the level count (N) while meeting harmonic distortion limits. The total harmonic distortion (THD) for a phase voltage approximates:

$$ THD \approx \frac{1}{2\sqrt{3}N} $$

For example, reducing N from 10 to 5 doubles THD but cuts SM costs by 50%. Advanced modulation techniques (e.g., nearest-level control) can mitigate THD penalties at lower N.

Case Study: HVDC vs. Industrial Drives

In Siemens’ HVDC PLUS systems, 200+ SMs per arm achieve THD <1.5%, justified by transmission efficiency gains. Conversely, ABB’s ACS6000 drives use ~12 SMs/arm, prioritizing cost savings for industrial motor control where THD <5% is acceptable.

Emerging Cost-Reduction Strategies

MMC Scalability Trade-offs A diagram illustrating the trade-offs between submodule count (N), DC-link voltage (V_dc), and capacitor voltage (v_c) in Modular Multilevel Converters (MMCs). Includes a graph of THD vs. N with cost scaling. MMC Arm Configurations N=5 v_c = V_dc/5 N=10 v_c = V_dc/10 N=200 v_c = V_dc/200 V_dc Performance vs. Cost Number of Submodules (N) THD (%) THD ≈ k/N Cost Industrial Drives HVDC Capacitor Voltage: v_c = V_dc/N
Diagram Description: The diagram would show the relationship between submodule count (N), DC-link voltage (V_dc), and capacitor voltage (v_c) across different MMC configurations.

5.3 Emerging Technologies and Innovations

Wide-Bandgap Semiconductor Integration

The adoption of silicon carbide (SiC) and gallium nitride (GaN) devices in MMCs has significantly improved efficiency and power density. These wide-bandgap (WBG) materials exhibit lower conduction losses, higher thermal conductivity, and faster switching speeds compared to traditional silicon-based IGBTs. For instance, SiC MOSFETs reduce switching losses by up to 80%, enabling MMCs to operate at higher frequencies (20–100 kHz) without compromising efficiency. The reduced thermal stress also allows for compact designs, critical for applications like offshore wind farms and electric aircraft.

$$ P_{loss} = R_{ds(on)} \cdot I_{rms}^2 + \frac{1}{2} V_{ds} \cdot I_{ds} \cdot (t_{rise} + t_{fall}) \cdot f_{sw} $$

Advanced Modulation Techniques

Recent innovations in modulation strategies, such as nearest-level modulation (NLM) and phase-shifted carrier PWM (PSC-PWM), optimize harmonic performance and reduce capacitor voltage ripple. NLM minimizes computational overhead by approximating the reference voltage to the nearest discrete level, while PSC-PWM distributes switching losses evenly across submodules. Hybrid modulation schemes, combining NLM with selective harmonic elimination (SHE), further reduce total harmonic distortion (THD) to below 2% in high-voltage applications.

Artificial Intelligence for Predictive Control

Machine learning algorithms, particularly long short-term memory (LSTM) networks and reinforcement learning (RL), are being deployed for real-time fault detection and dynamic voltage balancing. LSTMs predict submodule capacitor voltage deviations with 95% accuracy by analyzing historical switching patterns, while RL-based controllers adapt to grid disturbances within milliseconds. A case study in HVDC systems demonstrated a 30% reduction in recovery time during DC faults using these methods.

Solid-State Circuit Breakers

Integrating solid-state circuit breakers (SSCBs) with MMCs addresses fault isolation challenges in DC grids. SSCBs leverage WBG devices to interrupt fault currents within microseconds, compared to conventional mechanical breakers (5–10 ms). The energy absorption capability is derived from:

$$ E_{absorb} = \frac{1}{2} C_{eq} \cdot \Delta V^2 $$

where \( C_{eq} \) is the equivalent capacitance of the MMC arm. This innovation is pivotal for protecting multi-terminal HVDC networks.

Wireless Power Transfer Integration

MMCs are being adapted for dynamic wireless power transfer (DWPT) systems in electric vehicle charging. By using resonant inductive coupling at 85 kHz, MMCs achieve 92% efficiency over 15 cm air gaps. Key innovations include:

Digital Twin Technology

High-fidelity digital twins of MMCs, built using real-time simulators like RT-LAB or Typhoon HIL, enable predictive maintenance and performance optimization. These models incorporate:

Superconducting MMCs

Experimental MMCs employing high-temperature superconductors (HTS) in DC busbars reduce resistive losses to near-zero levels at 77 K. The critical current density \( J_c \) of YBCO tapes (1 MA/cm² at 77 K) allows for unprecedented current densities in compact designs. Challenges remain in cryogenic cooling system integration and quench protection.

6. Key Research Papers and Articles

6.1 Key Research Papers and Articles

6.2 Recommended Textbooks and Manuals

6.3 Online Resources and Tutorials