MMC-HVDC Transmission Using Modular Multilevel Converters

• MMC-HVDC transmission is a technology employing modular multilevel converters with distributed submodules to achieve superior voltage waveform quality and scalable high-voltage DC power.
• Advanced control methods, including direct and indirect modulation with predictive algorithms, reduce switching frequency by up to 80% and improve transient response.
• Integrated energy control and protection strategies, featuring fault ride-through and hybrid simulation, ensure reliable operation in both weak and strong grid conditions.

Modular Multilevel Converter-Based High-Voltage Direct Current (MMC-HVDC) Transmission is a foundational technology for large-scale, long-distance and multi-terminal DC transmission, particularly for renewable energy integration such as offshore wind. The architecture leverages distributed submodules to achieve superior voltage waveform quality, scalability in voltage and power ratings, and controllable energy storage and transient performance. Recent advancements center on energy control for fault ride-through, hybrid simulation, optimized modulation, resonance identification, protection strategies, and next-generation submodule topologies.

1. System Architecture and MMC Fundamentals

MMC-HVDC systems employ a modular converter topology, wherein each phase-leg incorporates an upper and lower arm, each assembled from $N$ series-connected submodules (SMs). The most widely adopted submodule is the half-bridge, comprising two IGBTs (or MOSFETs), antiparallel diodes, and a DC capacitor $C_{sm}$ (Kumar et al., 22 Nov 2025). The arms further embed inductances $L_{arm}$ for circulating current suppression.

A typical two-terminal point-to-point application is an offshore wind farm connected via submarine HVDC cable (±320 kV, 420 MW)—with a sending-end MMC on the offshore platform regulating voltage and frequency (V/f control) and a receiving-end MMC regulating DC link voltage and interfacing with the onshore AC grid. The module count, capacitance, and arm reactance are dimensioned to accommodate both steady-state modulation requirements and transient energy balancing. For example, in a 420 MW system, N=76 SMs/arm, C_sm=3000 μF, V_c,nom=8.42 kV (Kumar et al., 22 Nov 2025).

2. MMC Control Methodologies and Modulation Optimization

2.1. Modulation Index Quantification and Scheme Selection

Direct and indirect modulation strategies define the instantaneous arm-voltage references as a function of output and SM voltages. Direct modulation yields the largest linear PQ operating region and maximal AC output voltage, while indirect modulation—utilizing closed-loop capacitor voltage and circulating current suppression control—offers improved balancing and tighter THD (Sun et al., 9 Feb 2025). With closed-loop controls, direct and indirect modulation converge in steady-state.

Mathematically, the direct modulation index is $M_{ref1} = \frac{\sqrt{2}U_{ref1}}{U_{capN}}$, bounded by $M_{ref1} \leq 1$ to preserve linearity. Indirect modulation is defined as $M_{conv1} = \frac{\sqrt{2}U_{conv1}}{U_{dcN}/2}$, where limits are set by reference-wave constraints and transformer reactance. Optimal modulation can extend AC voltage capability by 5–10% vs. conventional schemes (Sun et al., 9 Feb 2025).

2.2. Switching Frequency Minimization

Advanced predictive control algorithms, such as lexicographic sorting (F1–V2), integrate previous switching states to minimize SM switching events in each cycle (Khanal et al., 2019, Khanal et al., 2019). Constrained multi-objective optimization guarantees capacitor voltage balancing, exact AC-current tracking and circulating-current suppression, while bounding the number of switches per sampling instant ($\overline{N_{sw}}$). Up to 80% reduction in device switching frequency is achievable, translating into substantial converter loss reductions and extending semiconductor lifetime (Khanal et al., 2019).

3. Energy Control Strategies and Fault Ride-Through

Onshore AC faults (single-phase or three-phase) cause the onshore active power export $P_{AC}$ to collapse while the wind farm continues to inject $P_{wind}$, creating a surplus power $P_s = P_{wind} - P_{AC}$. Without mitigation, the DC-link voltage $V_{dc}$ rapidly exceeds safety limits (up to 1.1 p.u. in <50 ms) (Kumar et al., 22 Nov 2025).

A two-stage energy control scheme is implemented:

• Stage 1: Dynamic storage of surplus energy in SM capacitors through modulated DC offset, raising $v_{c,j}$ and absorbing $P_s$.
• Stage 2: Activation of an energy dissipation device (EDD, e.g., resistive chopper), governed by $P_{EDD}(t) = k_{EDD}(V_{dc}(t)-V_{ref})^2$ when $V_{dc}$ and SM voltages exceed threshold.

Sizing equations prescribe $C_{sm}$ for energy absorption: $$C_{sm} \geq \frac{2\Delta E_{req}}{3N(V_{c,max}^2 - V_{c,nom}^2)}$$ and $P_{EDD,\max}$ for surplus dissipation. Simulations confirm reliable clamp of $V_{dc}$ below 1.1 p.u. in severe LLL-G faults (Kumar et al., 22 Nov 2025).

4. Small-Signal Impedance, Resonance, and Stability Criteria

MMC-HVDC systems exhibit multi-frequency responses owing to harmonics in arm currents and capacitor voltages. Harmonic State-Space (HSS) modeling permits explicit calculation of small-signal impedance $Z_{MMC}(j\omega)$, incorporating steady-state and control-induced harmonics up to sideband order $h$ (Lyu et al., 2017).

Key resonance modes include:

• Fundamental ($\sim$fgrid): Dominated by $L_{arm}$ and $N C_{sm}$
• Low-frequency circulating current (20–30 Hz): Damped by circulating current controller gain $R_a$
• Higher-order harmonics: Modified by AC voltage control bandwidth

Grid interaction analysis utilizes impedance ratio $L(j\omega) = Z_{grid}(j\omega) / Z_{MMC}(j\omega)$; instability arises if Nyquist contour encircles $-1$ (Radecic et al., 12 Nov 2025). For weak grids and long cables, resonances occur in the sub-synchronous region (75–90 Hz); strong grid/short cables shift resonances higher (600 Hz), with damping determined by controller bandwidth and protection logic (Radecic et al., 12 Nov 2025). Controller tuning (e.g., $R_a$ for circulating current, $K_pv$/$K_rv$ for voltage control) is essential.

5. Hybrid Simulation Frameworks and System-Level Validation

EMT-domain modeling of MMCs captures high-frequency internal dynamics but suffers from computational scale. Hybrid EMT–TS co-simulation frameworks—coupling PSCAD and PSS/E—enable scaling to large transmission networks (2002.01511). Fast ($\Delta t_{EMT}=60\mu s$) and slow ($4\mu s$) line discretizations permit trade-off between high-frequency fidelity and simulation speed. Voltage-sensitivity driven buffer-area sizing (e.g., $\Delta V_i/\Delta Q > 1.4\%/1000$ MVAr) stabilizes boundaries (2002.01511). Best practices call for slow-line and large buffer for high-fidelity, protection studies; fast-line with smaller buffer for preliminary screening.

6. Grid-Forming and System-Wide Control Strategies

Dual-port grid-forming (GFM) control leverages the MMC’s bidirectional architecture, enabling simultaneous control of AC and DC terminal voltages and regulating the converter’s internal stored energy $W_t$ (Groß et al., 2021). Control laws couple energy deviation to frequency (AC side) and DC voltage setpoint: $$\dot{\theta} = \omega^* + k^w_{ac}(W_t - W^*_t), \quad V_{dc}^* = V_{dc,ref} + k^w_{dc}(W_t - W^*_t)$$ Hybrid droop and energy-balancing variants are both stable across grid stiffness scenarios. Unlike single-port GFM, dual-port does not require prior AC/DC GFM/GFL role assignment, and achieves autonomous power rebalancing under severe contingencies.

Hierarchical OPF-integrated droop control can further embed AC frequency regulation into MTDC transmission, balancing generation cost minimization with tight DC voltage deviations (Du et al., 6 May 2025). Quasi-static input–output models guide optimal setpoint dispatch with practical secondary control via real-time primal-dual dynamics (Abdolmaleki et al., 10 Feb 2025). Event-triggered communication schemes reduce networked control traffic by up to 80% without performance loss.

7. Protection Strategy and Advanced Submodule Topologies

Differential protection for MMC-HVDC collector cables faces new sensitivity/selectivity challenges due to IBR-dominated fault current signatures (Davi et al., 23 Jan 2026). Enhanced 87Q/87G sequence-component protection recovers sensitivity to asymmetrical faults, contingent on converter negative-sequence current injection. Coordination of transformer grounding and adaptive bias slope tuning is recommended.

Emergent submodule architectures, such as Direction-Selective Parallel (DiSeP), enable sensorless bidirectional capacitor balancing and bipolar output with minimal device count (four transistors, four diodes per module) (Zhang et al., 23 Sep 2025). Switched-capacitor energy exchange and reduced impedance are achieved without sacrificing harmonic performance. Efficiency peaks at 96.3%, THD+N $\approx$ 10.3% in laboratory prototypes; proper selection of module capacitance, switch, and balancing inductance is necessary for HVDC scaling.

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Selected Parameter Overview

System	N/arm	C_sm	V_dc	Rated P	Dominant Resonance	Peak Efficiency
Two-terminal	76	3,000 µF	±320 kV	420 MW	75–90 Hz (weak)	96.3% (DiSeP)
MMC-HVDC test	6	2.5 mF	60 kV	50 MVA	20–30 Hz, 600 Hz	N/A

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Concluding Remarks

MMC-HVDC transmission architectures integrate advanced energy control, modulation, resonance management, hybrid simulation, grid-forming strategies, protection, and power-electronics topology. Recent research substantiates robust fault ride-through, near-optimal modulation-index utilization, minimized switching losses, stable operation under weak/strong grid conditions, and scalable secondary control and protection logic. The field continues to evolve toward higher efficiency, modularity, and reliability for both point-to-point and multi-terminal DC transmission (Kumar et al., 22 Nov 2025, Davi et al., 23 Jan 2026, Khanal et al., 2019, Sun et al., 9 Feb 2025, Lyu et al., 2017, Radecic et al., 12 Nov 2025, 2002.01511, Groß et al., 2021, Du et al., 6 May 2025, Abdolmaleki et al., 10 Feb 2025, Zhang et al., 23 Sep 2025).