[Paper Review] Distributed Controllers for Multi-Terminal HVDC Transmission Systems

Martin Andreasson, Dimos V. Dimarogonas+2 more|arXiv (Cornell University)|Nov 7, 2014

HVDC Systems and Fault Protection22 references4 citations

TL;DR

This paper proposes three novel distributed controllers for multi-terminal HVDC (MTDC) systems that ensure asymptotic stability and minimize a quadratic cost of current injections. By leveraging communication between buses with a graph-matching topology, the controllers stabilize voltages near nominal values and achieve optimal current sharing, as validated in simulations on a four-bus system with guaranteed convergence and bounded voltage deviations.

ABSTRACT

High-voltage direct current (HVDC) is an increasingly commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper the voltage-droop method (VDM) is reviewed, and three novel distributed controllers for multi-terminal HVDC (MTDC) transmission systems are proposed. Sufficient conditions for when the proposed controllers render the equilibrium of the closed-loop system asymptotically stable are provided. These conditions give insight into suitable controller architecture, e.g., that the communication graph should be identical with the graph of the MTDC system, including edge weights. Provided that the equilibria of the closed-loop systems are asymptotically stable, it is shown that the voltages asymptotically converge to within predefined bounds. Furthermore, a quadratic cost of the injected currents is asymptotically minimized. The proposed controllers are evaluated on a four-bus MTDC system.

Motivation & Objective

• Address the limitations of decentralized voltage droop control (VDM) in MTDC systems, such as static voltage errors and suboptimal current distribution.
• Overcome the lack of scalability and performance in existing decentralized methods by introducing communication-aware distributed control strategies.
• Ensure asymptotic stability of the closed-loop system under realistic communication and network constraints.
• Minimize a quadratic cost function of injected currents while maintaining voltages within predefined bounds.
• Design controllers that are fully distributed or require minimal centralized coordination, enabling practical deployment in future MTDC grids.

Proposed method

• Propose three distributed controllers (I, II, III) that use local voltage and current measurements combined with inter-bus communication to adjust injected currents.
• Design controllers based on a consensus-like structure where each bus updates its control input using weighted differences in voltage deviations from nominal values.
• Introduce controller gains (proportional and voltage feedback) and communication weights that are matched to the physical network's resistance and capacitance parameters.
• Ensure stability by requiring the communication graph to exactly match the physical MTDC network graph, including edge weights, to guarantee asymptotic stability of the equilibrium.
• Use a Lyapunov-based stability analysis to derive sufficient conditions for asymptotic stability, involving products of diagonal matrices and Laplacian matrices.
• Implement controllers with time delays in remote information exchange (e.g., 500 ms delay) to reflect real-world communication constraints in simulations.

Experimental results

Research questions

• RQ1 Under what conditions can distributed controllers stabilize the equilibrium of an MTDC system with voltage droop control and communication?
• RQ2 How can communication between buses improve voltage regulation and current sharing compared to conventional decentralized VDM?
• RQ3 What is the role of the communication network topology in ensuring stability and performance of distributed MTDC controllers?
• RQ4 Can a quadratic cost function of injected currents be asymptotically minimized while maintaining voltage bounds in a distributed MTDC control framework?
• RQ5 How do different controller architectures (centralized measurement, complete network, fully distributed) compare in terms of performance and implementation requirements?

Key findings

• The proposed controllers achieve asymptotic stability of the closed-loop system when the communication graph exactly matches the physical MTDC network graph, including edge weights.
• Voltages converge to within predefined conservative bounds, as demonstrated by Lemma 1 and confirmed in simulations with dashed-line bounds in Figure 3.
• All controllers successfully minimize a quadratic cost function of injected currents, with Controller III achieving this in a fully distributed manner without requiring a dedicated voltage bus.
• Controller I requires a dedicated voltage measurement bus, while Controller II requires a complete communication network, but both achieve stable voltage regulation and optimal current sharing.
• Simulations on a four-bus MTDC system show that all controllers achieve stable convergence: voltages remain within bounds and injected currents track optimal values after a step change in load.
• Sufficiently small γ and δ, along with large enough kP and min_i K^V_i, ensure that the stability conditions (22)–(24) are satisfied, enabling systematic controller gain selection.