DC-Grid Cooperation in Hybrid AC/DC Networks

• DC-Grid Cooperation is a framework that integrates architecture, unified modeling, and control techniques to enable seamless interaction between AC and DC power networks.
• It leverages advanced converter technologies and dual-port grid-forming controllers to balance energy exchange and ensure system stability across hybrid grids.
• Cooperation strategies incorporate distributed and hierarchical control, modular designs, and robust fault management for reliable grid restoration and islanding operations.

DC-Grid Cooperation refers to the set of principles, architectures, and control strategies enabling seamless and resilient interaction between direct current (DC) and alternating current (AC) power networks, with a special emphasis on hybrid AC/DC networks, multi-terminal DC grids, and converter-dominated infrastructures. It covers architectural, modeling, control, and information-structural aspects that facilitate robust and coordinated power exchange, ancillary services, and fault recovery across the AC/DC interface. Achieving high-performance DC-grid cooperation depends crucially on converter technologies, unified dynamic/steady-state modeling, distributed control, information structures, and rigorous stability and resilience guarantees.

1. Converter Architectures and Unified Control Formulations

Central to DC-grid cooperation is the deployment of interconnecting converters with advanced control laws that simultaneously provide grid-forming (GFM) and grid-following (GFL) functionalities for both AC and DC terminals.

Recent work formalizes the "dual-port grid-forming control" paradigm, exemplified by universal dual-port GFM controllers that treat each voltage-source converter (VSC) as a device with distinct AC and DC ports: an AC-side filter interfacing with the synchronous grid and a DC-link capacitor interfacing with the DC subgrid. The averaged device model is governed by the DC-link energy balance equation:

$$C\,v_\mathrm{dc}^\star\,\dot v_\delta = -P_{\delta,\mathrm{ac}} + P_{\delta,\mathrm{dc}}$$

with the key innovation being that all reference formation (AC phase angle, frequency, DC voltage) is derived from DC-link voltage deviation without recourse to classical phase-locked loops.

The universal dual-port GFM law is implemented as a proportional-integral (PI) controller on $v_\delta$, achieving both fast droop and inertia-like terms. This design unifies AC grid-forming (angle/frequency setting) and DC grid-following (voltage stabilization) in a single law with analytically guaranteed stability under mild parameter constraints, independently of specific network topology. This controller eliminates mode switching and enables any converter to serve as a slack for both AC or DC grids as needed (Subotić et al., 2023).

Complementary architectures, such as dual-port grid-forming converters in hybrid AC/DC grids, further generalize the cooperation principle by regulating both the AC-side voltage/frequency and the DC-side voltage using energy deviation in the converter. Internal energy storage is leveraged to tightly couple the AC and DC droop loops, with derivative augmentation for enhanced damping. In all modern dual-port schemes, passivity- and small-signal-based stability proofs underpin robust operation across a wide range of operating points, even in deeply hybridized and storage-rich grids (Arévalo-Soler et al., 30 Apr 2024).

2. Multi-Terminal, Hybrid, and Modular AC/DC Grid Modeling

Full DC-grid cooperation demands unified modeling frameworks encompassing both AC and DC network elements, all converter types, and their dynamic interactions.

Current methodologies move away from treating AC and DC grids as disjoint analytical entities, instead employing end-to-end graph-theoretic models with device plug-in by network reduction (graph plus Kron-reduction), as in the dual-port GFM framework (Subotić et al., 2023). Each device—synchronous machine, VSC, wind turbine, PV, battery, load—is described by linearized or reduced-order models attached via incidence matrices to the graph.

A key development is the transformation of hybrid AC/DC grid steady-state analysis into a single augmented AC system using two precise lemmas: (i) phase alignment of reflected DC-side variables in the AC reference frame, and (ii) enforced local reactive balance using shunt compensation, enabling the hybrid grid solution to emerge from a single Newton–Raphson solve on the augmented admittance. This approach directly preserves all original power allocations and substantially reduces computational effort, as only one solution of size $N_{ac} + N_{dc}$ is required, with a reduction in simulation time by approximately 48% compared to classical two-stage approaches (Rezvani et al., 2019).

In multi-terminal DC (MTDC) and extremely hybridized networks, modular virtual power plant (DVPP) designs—where multiple AC or DC modules (each potentially an aggregate of DERs) are recursively coupled via dynamic participation factors and linear droop transfer functions—provide a scalable route to full grid cooperation. Disaggregation of aggregate GFM performance objectives to all constituent modules preserves both robustness and plug-and-play scalability (He et al., 18 Oct 2024).

3. Distributed and Hierarchical Control, Information Structures, and Passivity

Distributed, hierarchical, and modular control architectures are pivotal for scalable DC-grid cooperation.

Plug-and-play distributed controllers, often synthesized through composite Lyapunov methods, allow arbitrary numbers and types of power-electronic devices (PV, battery, supercapacitor, EV charger, etc.) to be integrated or removed from DC (and hybrid) grids with minimal coordination, provided global references (e.g., DC bus setpoint, AC $P/Q$ targets) are periodically communicated. The system-of-systems viewpoint is realized by making each converter an “agent” governed by local state feedback and minimal global information, guaranteeing network-level stability by compositional Lyapunov arguments (Iovine et al., 2016, Iovine et al., 2016).

In larger or multi-agent (prosumer-based) DC networks, fully decentralized primal–dual controllers are directly linked to convex social-physical optimization objectives (incorporating grid technical constraints, user flexibility, and social value considerations). Passivity properties of the plant-controller interconnection guarantee global convergence to the welfare-optimal steady state, with all voltage and current bounds rigorously enforced (Cucuzzella et al., 2019).

Information structure analysis reveals that AC/DC grids, under both simple current-controlled and balanced dq-frame converter models, possess poset-causal (partially ordered set-causal) topologies, where all cross-domain coupling transpires through converter control inputs. This property systematically decomposes controller design over the AC and DC subsystems, dramatically simplifying decentralized $\mathcal{H}_2$ optimization, particularly in coordinated and leader-follower MTDC layouts (Taylor, 2023).

4. Advanced Operation: Islanding, Fault Management, and Grid Restoration

DC-grid cooperation underpins advanced operational strategies such as controlled islanding and seamless resynchronization.

In the controlled islanding of hybrid AC/DC grids with VSC-HVDC links, cooperation is achieved by strategic assignment of DC terminals to separate islands. Post-fault, the DC link becomes the exclusive tie for power exchange, enabling post-islanding power balancing and minimization of generation-load imbalances with optimal spectral clustering. This approach is validated via large-scale simulation and real-time hardware-in-the-loop tests, and demonstrates rapid, robust system recovery (Li et al., 2018).

Grid-aware islanding and resynchronization frameworks generalize AC/DC cooperation by embedding unified hybrid AC/DC load flow models, sensitivity-based OPF formulations, and fast-control state-machines for transition management. Converter interfacing becomes grid-forming or grid-following dynamically, leveraging DC grid multiterminality for flexible power slack provision and smooth recovery over both AC and DC subgrids, with all network, converter, and resource constraints enforced at 1 Hz solution rates. Experimental evidence indicates constraint violations are avoided throughout all transition phases, and system transients are eliminated due to consistent pre- and post-switch OPF solutions (Lambrichts et al., 6 Mar 2025).

5. Performance, Stability, and Practical Tuning Guidelines

Performance and robust stability of cooperative DC-grids are analytically tractable in modern controllers.

Dual-port GFM schemes possess explicit small-signal stability theorems, with parameter selection—particularly the relative sizing of proportional and integral gains—directly related to network capacitance, resistance, and connectivity, independent of detailed topology. Stability is demonstrated over broad conditions, with closed-form Lyapunov functions and block-diagonal structures (Subotić et al., 2023, Arévalo-Soler et al., 30 Apr 2024).

In practice, typical DC/AC droop gain selection achieves closed-loop bandwidths of 5–20 Hz; differential (derivative) droops can be tuned to achieve damping ratios $ζ \geq 0.6$. In multi-terminal settings, ensuring proportional sharing and bounded deviations in stored energy require matched droop slopes (within 10%), and sufficient energy margin in converter storage. Laboratory and large-scale simulation studies confirm that high-power transients, islanding events, or grid formation/loss do not destabilize the system when guidelines are adhered to.

Plug-and-play architectures, primal–dual optimal controllers, and modular DVPP decompositions are robust to device-level nonlinearities, reference changes, and certain classes of exogenous disturbances—so long as the physical grid remains connected and technical feasibility assumptions are satisfied (Cucuzzella et al., 2019, He et al., 18 Oct 2024).

6. Extensions, Open Challenges, and Future Directions

Present frameworks address a significant part of the DC-grid cooperation challenge, yet several extensions are actively being investigated:

• Extension of steady-state unification strategies to include full nonlinear converter dynamics, time-varying phase shifts, and on-line adaptation for multi-terminal and meshed DC networks (Rezvani et al., 2019).
• Generalization of information-structure-based modular controller design to large-scale and mission-critical AC/DC grid deployments.
• Incorporation of detailed finite-bandwidth converter models, with loss dynamics and hard saturation, into grid-scale optimal and distributed control frameworks.
• Development of adaptive tuning techniques for droop and virtual impedance parameters in real time, especially for highly variable DER portfolios.
• Coordinated control for multi-terminal HVDC grids, advanced protection/fault-ride-through schemes, and integration with cyber-physical security and communication networks.

Continued research at the intersection of advanced converter control, unified modeling, passivity-based design, information-structural decomposition, and optimization-based operation will drive the evolution and resilience of future hybrid AC/DC grids (Subotić et al., 2023, He et al., 18 Oct 2024, Lambrichts et al., 6 Mar 2025, Taylor, 2023).