The eastern coastal provinces of China present a distinctive operating environment for frequency stability because their load growth has been matched not by local synchronous generation but by an expanding portfolio of long-distance direct current links. Each new infeed displaces the rotating machines that historically supplied the grid’s kinetic energy reserve, so the same disturbance that once produced a modest frequency excursion now produces a steeper initial decline. The rate of change of frequency, or RoCoF, is the quantity that captures this steepness most directly: it reflects the instantaneous balance between electrical power demand and the mechanical or converter-delivered power feeding the bus, divided by the system inertia. When inertia falls, the same power imbalance produces a larger RoCoF, which means the initial slope of the frequency trajectory becomes an informative signal about how severe the eventual excursion will be.

This observation underlies the central analytical contribution of the study. Rather than waiting for the frequency to reach its nadir and then reacting, the authors derive a mapping from the RoCoF measured at the converter bus in the first moments after a disturbance to the maximum frequency deviation that will follow. The derivation proceeds from a primary frequency regulation model of the receiving-end grid, in which the aggregated behavior of synchronous machines, their governors, and the loads is reduced to a tractable form. Solving the resulting differential relationships shows that the initial RoCoF encodes enough information about the magnitude and location of the disturbance to bound the subsequent trajectory. This is a significant practical advantage over earlier nadir-prediction techniques, which relied on polynomial fitting of extended time-series records of the frequency response. Those fitting methods can be accurate, but they require a substantial window of measured data before producing an estimate, and their performance degrades when the input record is incomplete. By contrast, a RoCoF-based estimate is available essentially immediately, which is precisely the timescale on which converter control decisions must be made.

The physical rationale for using converter stations as the response mechanism deserves attention. A modular multilevel converter does not possess inherent inertia in the sense that a synchronous machine does; its energy is stored in DC-link capacitors and submodule capacitors, and its power output is set by control commands rather than by electromechanical dynamics. However, through the control layer the converter can be made to emulate inertial and damping behavior. The paper describes two implementation routes. When the station operates under constant active power control, the d-axis outer-loop reference is augmented with terms proportional to the frequency deviation and its derivative, scaled by a damping coefficient and a virtual inertia coefficient respectively. When the station instead holds the DC voltage constant, the same frequency-regulation characteristic can be achieved by shaping the DC voltage reference, exploiting the approximate differential relationship between DC-side energy storage and AC-side power output. In both cases the converter behaves, from the perspective of the AC bus, like a controllable source of fast frequency support whose responsiveness is limited mainly by the converter’s current rating and the DC network’s power transfer capability.

The three-stage structure of the frequency response motivates the adaptive timing logic. In the inertial stage, immediately after a disturbance, frequency is moving rapidly away from nominal and the priority is to arrest that motion; virtual inertia support, which responds to the derivative of frequency, is the appropriate tool because it injects power in proportion to how fast the frequency is falling. In the damping stage, the frequency has passed its extreme point and is returning toward a new equilibrium; continued inertia support at this point would actually oppose the recovery, since the derivative term reverses sign as the frequency climbs back. Damping support, which responds to the frequency deviation itself, is the correct tool here because it sustains power output in proportion to how far the frequency remains from nominal, accelerating convergence to the steady state without fighting the natural recovery. The steady-state stage then requires no dynamic support beyond whatever droop-like contribution maintains the new equilibrium.

What distinguishes the proposed strategy from conventional fixed-parameter schemes is that the virtual inertia and damping coefficients are not constants chosen in advance for a worst-case design scenario. Instead, they are tuned dynamically as functions of the measured initial RoCoF, using the derived mapping to anticipate how large the frequency excursion will be. A small disturbance, indicated by a gentle RoCoF, calls for a modest response, preserving converter headroom and avoiding unnecessary power swings. A severe disturbance, indicated by a steep RoCoF, calls for an aggressive response concentrated in the inertial stage, when it does the most good. This anticipatory quality addresses a known weakness of fixed-parameter virtual synchronous machine control: a single parameter set must compromise between the needs of the first seconds and the needs of the following tens of seconds, and that compromise inevitably leaves performance on the table in one phase or the other.

The validation on a modified IEEE 39 bus system is a meaningful choice of testbed. The 39 bus system, derived from the New England transmission network, is a well-established benchmark with ten machines and a rich set of inter-area and local oscillation modes, and modifying it to include MMC-HVDC infeed allows the interaction between converter control and synchronous machine response to be examined under realistic network conditions. The simulation results reported in the paper confirm that the adaptive strategy limits the maximum frequency deviation more effectively than fixed-parameter alternatives while also supporting a faster recovery, which is exactly the dual objective that the two-stage support logic was designed to achieve.

Several broader considerations frame the significance of this work. First, the authors are affiliated with the State Key Laboratory of HVDC at the Electric Power Research Institute of China Southern Power Grid, which operates one of the world’s largest portfolios of HVDC infeeds into coastal load centers; the problem studied is not hypothetical but a daily operational reality for a grid in which the share of power delivered by DC links continues to grow. Second, the approach requires no new hardware, no communication links beyond local frequency measurement, and no changes to the sending end of the DC link, which makes it deployable as a control-layer upgrade to existing stations. Third, because the mapping from RoCoF to maximum deviation is derived analytically from a primary frequency regulation model rather than learned from data, it remains interpretable and can be recalibrated as the grid’s composition changes, an important property for a system whose inertia is steadily declining.

The work also sits within a wider research conversation about how converter-dominated grids can maintain frequency stability. Virtual synchronous machine control and droop-based frequency support have been studied extensively, and coordinated schemes that distribute frequency support duties among multiple onshore converters, or that jointly manage DC voltage and AC frequency at a single station, have appeared in prior literature. The distinctive element here is the use of a predictive signal, the initial RoCoF, to schedule the support effort in time. In effect, the converter is given a forecast of how bad the disturbance will be before the frequency has finished falling, and it allocates its response accordingly. This converts the converter from a reactive follower of the frequency trajectory into an anticipatory participant in it, which is a qualitatively different mode of operation.

Looking forward, the framework suggests several natural extensions. The mapping between RoCoF and maximum deviation was derived for a primary frequency regulation model, and its accuracy under conditions involving protection actions, load shedding, or significant nonlinear behavior would merit further study. The strategy was validated in simulation on a single test system, and hardware-in-the-loop or field trials would be the next step toward operational adoption. Multi-station coordination, in which several receiving-end converters share the support duty according to their individual headroom and the RoCoF observed at their respective buses, is another direction that could amplify the benefit in grids with many parallel DC infeeds. Finally, as renewable generation connected through converters continues to expand on the sending end as well, the same RoCoF-based anticipatory logic could in principle be applied to sending-end stations and to grid-forming renewable plants, extending the concept beyond the receiving-end context in which it was developed.

Subject of Research: Adaptive active frequency support strategy for receiving-end MMC-HVDC stations based on rate of change of frequency

Article Title: Adaptive active frequency support strategy for receiving-end MMC-HVDC stations based on rate of change of frequency

Article References: Tian, B., Li, J., Zhai, H., & Zhang, Y. (2025). Adaptive active frequency support strategy for receiving-end MMC-HVDC stations based on rate of change of frequency. Frontiers in Electronics, 6, Article 1672188. https://doi.org/10.3389/felec.2025.1672188

Image Credits: AI Generated

DOI: 10.3389/felec.2025.1672188

Keywords: Adaptive, active, frequency, support, strategy, receiving-end, MMC-HVDC, stations, based, rate, change, scientific research