Cyber-Attacks Can Flip Power Flow in HVDC Transmission Lines, Study Finds

A small nudge to a voltage measurement could be enough to reverse the direction of bulk power flowing through a high-voltage direct-current transmission link, according to a new theoretical and simulation study published in the journal Autonomous Intelligent Systems. Researchers set out to map exactly where the steady-state operating points of a two-terminal HVDC system land when an attacker quietly corrupts the measurements that its controllers depend on, and their analysis reveals abrupt, bifurcation-like jumps in transmitted power triggered by surprisingly modest perturbations.

HVDC technology has become a backbone of modern grids, moving large amounts of electricity over long distances and integrating renewable generation. The study focuses on voltage-sourced converter HVDC systems, in which insulated gate bipolar transistors give operators fast, fine-grained control over power flow. That controllability, however, rests on a continuous stream of real-time measurements of DC voltage and DC power at each converter, collected by metering and communication devices that have been experimentally shown to be vulnerable to compromise.

The authors, led by Haonan Xu, model a two-terminal VSC HVDC link as two controllable DC power sources connected through a resistive transmission line with parallel capacitors. Each converter runs closed-loop proportional-integral controllers that continuously drive measured power and voltage toward preset references. A switching layer, implemented as min-max control selectors, then chooses among the outputs of the power controller, the voltage controller and a power-limit block, while inter-station coordination presets the references themselves. The result is a hierarchical, switching control architecture rather than a single fixed control law.

The attack model in the paper is deliberately conservative. The attacker needs no prior knowledge of control settings or line parameters, no read access to the system’s operating status, and no ability to alter the control references sent from the control center. The only capability assumed is limited write access to the measured feedback signals, allowing the attacker to add offsets to the measured DC voltages and powers. Mathematically, the authors show that adding an increment to a measured signal in a closed-loop controller is equivalent to adding the negative of that increment to the corresponding reference, which directly shifts the position of the system’s control curves.

The core analytical move is geometric. Each converter’s control behavior can be drawn as a curve in its own voltage-power plane: voltage control appears as a vertical line and power control as a horizontal line. But the two converters operate in different planes, so determining the system’s operating point requires mapping converter #1’s curves onto the plane of converter #2. The authors prove that this mapping distorts the geometry: the vertical voltage-control line of converter #1 becomes a quadratic curve in the common plane, and the horizontal power-control line becomes a curve involving a square root, or a piecewise combination of two such branches when the power reference is negative. The paper states that this is the first demonstration that originally linear HVDC control curves become quadratic or more complex when mapped onto a common control plane.

With the curves mapped into a single plane, the equilibrium points of the whole system are simply the intersections between converter #1’s mapped curve and converter #2’s own control lines. The authors derive propositions and a corollary that enumerate which control mode the system settles into under different attack conditions, covering combinations labeled 1P2U, 1U2U, 1P2P and 1U2P, where the notation indicates whether converter #1 is in power or voltage control and converter #2 likewise. Each combination of attack offsets on the measured power and voltage satisfies a different set of inequality conditions, and those conditions determine whether the equilibrium lies at the voltage-control intersection, the power-control intersection, or both.

Time-domain simulations in MATLAB/Simulink validate the theory. In the case study, the base values are 60 kV, 1 kA and 60 MW, with control references of 1 pu power at converter #1, minus 1 pu at converter #2, and DC voltage references of 1.1 pu and 1 pu. Two attacks are injected by perturbing the measured DC voltage U2: an offset of 0.1 pu at 5 seconds and 0.2 pu at 20 seconds. After the first attack, the system takes less than 15 seconds to shift from a positive power transfer of 1 pu to zero power transfer, meaning the sending AC grid can no longer export its generation while the receiving grid faces a severe deficit. After the second attack, the system takes roughly 2 seconds to swing from zero to a negative transfer of minus 1 pu, deepening the imbalance on both ends.

The simulations trace these dramatic swings to erroneous switching of converter control modes: the system moves from 1P2U control to 1U2U control after the first attack, and from 1U2U to 1U2P after the second. A geometrical visualization of the full landscape of equilibria under varying attack offsets shows four distinct control-mode regions. Within each region, transmitted power varies smoothly with the attack parameters, but at the boundaries the dependence remains continuous yet non-smooth, signaling bifurcations. The transition from 1P2U to 1U2P control appears as a steep cliff along which transmitted power rapidly flips from positive to negative, so small variations in attack magnitude near that boundary can induce large changes in power transfer.

The authors frame the work as a vulnerability assessment tool rather than a defense in itself. They note that dedicated cybersecurity standards tailored to HVDC systems are still in an early stage of development, and current industry practice tends to adapt generalized smart grid and industrial control system standards such as IEC 61850 and IEC 62351. By anticipating attack-induced HVDC behaviors and quantifying the resulting power imbalances, the proposed framework gives HVDC operators explicit means to evaluate operating risks before an incident. In the conclusion, the authors suggest mitigation paths including model-based anomaly detection using redundant sensors for cross-validation against power system physics, and data-driven detection that applies feature extraction such as principal component analysis to historical measurement datasets to catch stealthy intrusions.

The study’s scope carries clear limitations. The analysis covers two-terminal VSC HVDC systems, not multi-terminal networks, and the simulation results are numerical case studies rather than experiments on physical hardware. The attack model assumes only measurement perturbations, excluding attacks on references or control settings. Even so, the findings underscore a structural fragility: because HVDC links exist precisely to maintain power balances between AC grids, a control architecture whose operating point can jump discontinuously under small measurement errors deserves close attention from operators and standards bodies alike. The authors say future work will extend the equilibrium analysis to multi-terminal HVDC networks, where more intricate dynamics and richer patterns of attack-induced equilibria are expected to emerge.

Subject of Research: Cyber-attack-induced equilibrium shifts and control-mode switching in two-terminal VSC HVDC power transmission systems

Article Title: Cyber-attack-induced equilibria of high-voltage direct-current power transmission systems

Article References: Xu, H., Wei, Q., Li, K., Liu, X., Ding, Y., Zheng, D., Feng, K., Song, Y., & Hou, J. (2026). Cyber-attack-induced equilibria of high-voltage direct-current power transmission systems. Autonomous Intelligent Systems, 6(1), Article 12. https://doi.org/10.1007/s43684-026-00132-5

Image Credits: AI Generated

DOI: 10.1007/s43684-026-00132-5

Keywords: HVDC, cyber-attack, power systems, equilibrium points, control switching, VSC converter, bifurcation, measurement attack, grid security, power transmission, MATLAB Simulink, cyber-physical systems