One-minute frequency disturbances from unintended synchronization in cyber–physical power systems
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MainThe transition to a sustainable energy system requires advanced control methods to deal with increasing complexity and uncertainty1,2.
As variable renewable energy sources such as wind and solar replace conventional generation, maintaining power balance requires accurate forecasting and real-time control of storage, backup generation and flexible demand3.
At the same time, the electrification of sectors such as transport and heating is introducing millions of digitally controlled devices—electric vehicle chargers4, heat pumps5 and smart appliances6—into the grid. Furthermore, data centres add additional software-dependent loads7.
Together, these trends are reshaping the power system into a cyber–physical infrastructure, where physical devices and digital control are deeply intertwined.
In this new paradigm, system reliability increasingly depends not only on the physical properties of generation and load but also on the design, timing and coordination of software-controlled devices across all layers of operation8.While cyber–physical integration enables unprecedented levels of efficiency and flexibility, it also introduces new systemic risks9. Historical events underscore the stakes: inadequate situational awareness contributed to the 2003 North American blackout10, and software-driven control failures have played critical roles in recent major outages11,12.
Beyond failures and malicious attacks, however, even benign control routines can become systemically relevant when many devices act coherently.
Unintended synchronization can generate recurrent and potentially amplified oscillatory behaviour in large-scale cyber–physical energy systems.Modern power systems exhibit oscillations across a broad range of time scales. Oscillations with characteristic periods around 1 min have previously been discussed as ultralow-frequency oscillations (ULFOs) and linked to resonance phenomena in hydropower turbine-governor systems13,14,15,16.
However, resonance phenomena in classical control systems differ fundamentally from cyber–physical synchronization effects.
Oscillations without external timing signals do not naturally explain patterns that remain phase-coherent over long time scales or occur reproducibly across diverse power systems.In this Article, we identify and explain a coherent 1-min oscillation in power systems worldwide caused by cyber–physical synchronization effects. We show that the grid frequency, and thus the power balance, exhibits a highly regular periodic pattern with a period of exactly 1 min. Searching for potential causes of this pattern, we provide empirical evidence that clock-synchronized control actions in battery-based uninterruptible power supplies (UPSs) generate periodic power-demand peaks, and we demonstrate that this signal propagates across multiple voltage levels up to the transmission interface.
More broadly, our results point to a class of cyber–physical power oscillations driven by externally synchronized control software.The identified synchronization mechanism is not specific to UPSs or battery systems, but reflects a general property of digitally controlled devices operating with external timing signals or periodic software routines. The rapid expansion of battery storage, data-centre infrastructure and Internet-of-Things (IoT) devices increases the relevance of cyber–physical risks in power-system operation.
At the same time, decreasing system inertia makes power systems more sensitive to coherent power imbalances17.
Indeed, we observe that the amplitude of the 1-min pattern has increased in several grids. The oscillation contributes to wear and tear, especially in hydropower turbines18, and has motivated stricter load–frequency control requirements19. Our results indicate that coherent cyber–physical oscillations can be mitigated directly at their source through improved control design.A universal 1-min pattern in the grid frequencyThe grid frequency is a key observable in power-system operation, reflecting the balance between generation and load: it rises when generation exceeds demand and falls when demand outpaces supply. Maintaining the nominal frequency of 50 Hz or 60 Hz therefore requires continuous balancing by load–frequency control systems20.Large frequency deviations occur during contingencies and severe disturbances and can endanger system stability21,22.
Smaller but recurrent deviations arise continuously during normal operation through both stochastic fluctuations and deterministic mechanisms23,24.To identify dominant recurrent patterns, we carry out a Fourier analysis of grid-frequency time series f(t) from multiple power systems worldwide (Fig.
1).
The investigated grids span five continents and range in size from approximately 400,000 customers in Iceland to more than 400 million customers in the Continental European synchronous area.Fig.
1: Fourier spectra of the grid frequency f(t) for 12 grids on different continents that exhibit a 1-min pattern.Measurements for the Continental European, British, Scandinavian and Australian grids are taken at the transmission grid level, whereas measurements for the other grids are taken at the distribution grid level. Details on the data sources and processing are described in the Methods. The Fourier spectra are computed using SciPy’s Fast Fourier Transform implementation.Source dataRecurrent frequency deviations occur across a broad range of time scales. Figure 2 summarizes the dominant Fourier peaks and characteristic patterns observed in the Continental European grid.Fig. 2: Overview of recurrent frequency deviations in the Continental European power grid.a, The Fourier spectrum of the grid frequency exhibits pronounced peaks at different time scales. b, The peak at 60 min arises from electricity trading in hourly blocks26,27. Generation is rapidly adjusted at the beginning of each hour, leading to characteristic power imbalances and DFDs. The figure shows the resulting daily frequency profile together with load and stylized stepwise generation. Trading in shorter market intervals is increasing and gives rise to an additional peak at a period of 15 min (ref.
28).
c, This work focuses on the peak at exactly 1 min. We identify cyber–physical power oscillations caused by clocked control algorithms as the root cause of this pattern. A related but less stable pattern is observed at a period of approximately 100 s. The figure shows the corresponding waveforms for different months. d, Inter-area oscillations are electromechanical power swings between different regions of a synchronous grid and typically occur at periods of one to several seconds30. The figure shows an example recorded on 28 April 2025. e, Additional fast oscillatory phenomena include periodic power variations originating from data centres29,32 and subsynchronous oscillations in inverter-dominated grids33.Source dataAt slow time scales, pronounced peaks occur at periods of 15 min and 60 min together with their higher harmonics. These deterministic frequency deviations (DFDs) arise from electricity trading, where generation is adjusted approximately stepwise at the boundaries of market intervals while electrical demand evolves continuously25,26,27,28. This phenomenon is not unique to the Continental European grid; it also appears in other markets such as Scandinavia (cf.
Supplementary Fig.
1).Additional recurrent patterns occur at shorter time scales, including oscillations due to load variations in data centres29, inter-area oscillations between geographically separated groups of synchronous generators30 and persistent forced oscillations of previously unresolved origin31 with periods of one to a few seconds. At even faster time scales, recent studies have identified sustained oscillations related to interactions of grid dynamics and data centres32 as well as subsynchronous oscillations in inverter-dominated grids33.Against this background, we observe a remarkably narrow spectral peak at exactly 1 min in all investigated grids (Fig.
1).
The signal is particularly pronounced in large interconnected systems in Europe, North America and Australia, but remains clearly visible in smaller grids such as Malaysia, South Korea and South Africa, as well as in island systems such as Mallorca, Ireland and Iceland.
Its extremely narrow spectrum indicates a precisely timed and phase-coherent process that remains stable over multiple years.
Related oscillations with characteristic periods around 1 min have previously been described as ULFOs13. In addition, we observe a weaker peak around 100 s whose origin remains uncertain. What causes this universal 1-min pattern?Characterization of the 1-min patternTo characterize the universal 1-min pattern, we divide the frequency time series f(t) into chunks of length τ. For every chunk, we compute a characteristic minutely profile s(t), referred to as the waveform in the following. More precisely, s(t) is the average over all minutes in the respective chunk for a given second of the minute t (see the Methods for details). Typically, we use chunks of length τ = 1 h to remove the hourly patterns induced by market effects, indicated by the subscript h. Furthermore, we define the hourly amplitude as$${a}_{{h}}=\frac{1}{2}\left(\mathop{\max }\limits_{t}({s}_{{h}}(t))-\mathop{\min }\limits_{t}({s}_{{h}}(t))\right)$$ (1) to characterize the strength of the pattern.Figure 3a–c summarizes the waveform properties for the Continental European grid.
The amplitude exhibits a pronounced daily modulation, with weaker signals during the night and stronger amplitudes during daytime operation.
By contrast, the waveform shape remains remarkably stable: the frequency is typically highest at the beginning of the minute and then decreases for a few seconds (night) up to half a minute (day).
Comparable behaviour is observed across multiple grids (Supplementary Fig. 2), although the precise waveform shape differs between systems.Fig.