Stable Synchronization Research Articles

Stability of synchronization in simplicial complexes with multiple interaction layers.

Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in the presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic Rössler oscillators and Sherman neuronal models, and we demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.

The structure of uni-directional chain for the synchronization of networked chaotic systems

In this paper, we introduce the structure of uni-directional chain (UDC) as a benchmark to probe the synchronizability of networked chaotic system. By studying the relation between the length of UDC and its synchronizability, we identify a region of coupling strength, referred to as strong controllable region (SCR), where a UDC with arbitrary length could realize synchronization that is robust to non-local disturbance. More importantly, it is found that there exists a kind of chaotic oscillators where the region of negative master stability function (MSF) overlaps with the SCR. As MSF implements local stability analysis to provide the necessary condition for the appearance of synchronization, while SCR permits stable synchronization corresponding to non-local disturbance pertinent to sufficient condition, the role of MSF for such kind of oscillator may be equivalent to provide sufficient condition of network synchronization. Besides, we propose methods for the control of network synchronization based on the characteristic of UDC. For networks with fixed structure, by obtaining a minimal spanning tree, each node chooses one of its neighbors and follows its dynamics with uniform coupling strength to realize synchronization. For growing networks, by establishing directed connection from newly added nodes to existing nodes. An interacting structure which is similar to the combination of a group of UDCs is formed and the system is guaranteed to be controlled within the SCR.

Evaluating Small-Signal Synchronization Stability of Grid-Forming Converter: A Geometrical Approach

Grid synchronization stability is an important research topic for grid-forming converters. To prevent instability and undesired oscillations, the small-signal modeling and stability analysis must be performed, which requires the line impedance information. Nevertheless, the line impedance may be unknown in most cases. As a consequence, the designed control parameters may fail to satisfy the stability requirement. To fill in this research gap, this article presents a geometrical approach to evaluate and improve the small-signal synchronization stability of grid-forming converters. The proposed analytical approach maps the line impedance variation on a two-dimensional plane and identifies the stability boundary in a geometrical way. As a benefit, the controller of grid-forming converters can be explicitly designed to achieve the robust synchronization stability. Finally, the feasibility of the proposed technique is verified by simulation and hardware experimental results.

Research on Global Clock Synchronization Mechanism in Software‐Defined Control Architecture

Adopt software-definition technology to decouple the functional components of the industrial control system (ICS) in a service-oriented and distributed form is an important way for the industrial Internet of things to integrate information technology, communication technology, and operation technology. Therefore, this paper presents the concept of software-defined control architecture and describes the time consistency requirements under the paradigm shift of ICS architecture. By analyzing the physical clock and virtual clock mechanism models, the global clock synchronization space is logically divided into the physical and virtual clock synchronization domains, and a formal description of the global clock synchronization space is proposed. According to the fundamental analysis of the clock state model, the physical clock linear filtering synchronization model is derived, and a distributed observation fusion filtering model is constructed by considering the two observation modes of the virtual clock to realize the time synchronization of the global clock space by way of timestamp layer-by-layer transfer and fusion estimation. Finally, the simulation results show that the proposed model can significantly improve the accuracy and stability of clock synchronization.

Synchronization Stability of Grid-Following Converters Governed by Saturation Nonlinearities

Saturation nonlinearities caused by control limiters will be activated during large disturbances, complicating the stability of grid-tied voltage source converters (VSCs). This letter investigates the large-disturbance synchronization stability of the grid-tied VSC considering two typical control limiters, i.e., the hard limiter of the reference current and the circular limiter used to avoid overmodulation. A unified differential equation (UDE) model is proposed to quantify the transient responses and stability boundaries of the system under different saturation conditions. It is revealed that the VSC behaves as a current source when the hard limiter is activated; while the interaction between the two limiters drives the VSC to work as a voltage source, making it immune to synchronization instability.

Global Optimality of Inverter Dynamic Voltage Support

This paper investigates the dynamic voltage support (DVS) from inverter-based resources (IBRs) under voltage sags to enhance the low-voltage ride-through performance. The DVS problem is formulated as a nonconvex optimization program that maximizes the positive-sequence voltage magnitude at the point of common coupling (PCC) subject to the current, active power, and synchronization stability constraints. Then, we perform the optimality analysis to explore the global optimum analytically. It is found that the unique global optimum has three scenarios/stages (S1–S3), which depends on the specific relationship among grid voltage, grid strength, and physical limits of IBRs. The explicit closed-form solutions in S1 and S3 are derived, and the optimality conditions (an implicit solution) of S2 are provided, which guarantees the global optimality and enables the compatibility with fast real-time control. Finally, we implement the optimum with a grid-connected single-stage photovoltaic (PV) power plant by integrating a DVS controller. Dynamic simulations are carried out under different scenarios to test our proposal. The robustness against model errors is also discussed.

Power Compensation Control for DFIG-Based Wind Turbines to Enhance Synchronization Stability During Severe Grid Faults

Wind turbines (WTs) are prone to lose the synchronization during severe grid faults due to the absence of equilibrium point. To cope with the issue, this letter proposes a power compensation control for doubly fed induction generator based WT to enhance the transient synchronization stability from the new perspective of active power balance. In the method, the active power of WT is controlled to compensate the power loss on the network. Compared with the existing methods, the proposed method has more widely application scenarios because it avoids using the frequency error as control signal. Experimental tests are performed to validate proposed method.

Conductance-frequency droop control to ensure transient stability of inverter-based stand-alone microgrids

Currently, inverter-based stand-alone microgrids are gaining interest due to the advantages of obtaining energy from renewable sources. To manage the operation, these microgrids include storage systems connected in parallel to the PCC through electronic inverters that are controlled as voltage sources in order to support the frequency and voltage at the PCC. For the purpose of ensuring P and Q sharing among inverters and also the synchronization stability of the microgrid, droop control is widely used, achieving a satisfactory performance in normal operation. Nevertheless, in the presence of overloads or short-circuits, the inverters must limit the current for self-protection, thereby modifying the performance of the system that then becomes prone to suffer transient stability problems. In this paper, first the performance of the inverter-based stand-alone microgrids with the conventional P-f and Iact-f droops is analyzed, obtaining the stability boundaries during current limitation. In order to always ensure the synchronization stability of the system, this paper then proposes the G-f droop that consists in employing the equivalent conductance seen by each inverter for its frequency droop control. Furthermore, as this variable always correctly represents the inverter power angle, the system dynamics are not affected by the operating conditions. The theoretical results have been validated by means of simulation and Hardware-In-the-Loop results, showing the superior performance of the proposed G-f droop.

Back‐electromotive‐force observer (BEMF observer) based symmetrical PLL for grid synchronization stability enhancement under weak grid conditions

The synchronous reference frame phase-locked loop (SRF-PLL) is widely utilized for grid synchronization in voltage-source converter (VSC) system. However, it fails to eliminate the effect of high grid impedance leading to instability in weak grids. To address this issue, this paper introduces the back-electromotive-force observer (BEMF observer), commonly being utilized in DC motor, to modify the input of the SRF-PLL. To be specific, the equivalent internal electromotive force calculated by the BEMF observer rather than the PCC voltage is used to capture the phase information. Since the BEMF observer is designed in α β $\alpha \beta$ -frame while the SRF-PLL is in d q $dq$ -frame, the conventional stability analysis method suffers from complicated process. Thus, this paper further reconstructs the SRF-PLL with the BEMF observer to be symmetrical for simplification. Apart from the symmetrical structure, the stability criterion is accordingly modified. As a result, the proposed back electromotive force based symmetrical PLL (BEFS-PLL) offers the following advantages: (i) it effectively enhances the grid synchronization stability and simplifies the stability analysis process simultaneously, (ii) it exhibits a strong robustness even with the calculation error up to 50%, and (iii) it is characteristic of clear physical meanings. Finally, the effectiveness of the BEFS-PLL is verified by simulation.

When multilayer links exchange their roles in synchronization.

Real world networks contain multiple layers of links whose interactions can lead to extraordinary collective dynamics, including synchronization. The fundamental problem of assessing how network topology controls synchronization in multilayer networks remains open due to serious limitations of the existing stability methods. Towards removing this obstacle, we propose an approximation method which significantly enhances the predictive power of the master stability function for stable synchronization in multilayer networks. For a class of saddle-focus oscillators, including Rössler and piecewise linear systems, our method reduces the complex stability analysis to simply solving a set of linear algebraic equations. Using the method, we analytically predict surprising effects due to multilayer coupling. In particular, we prove that two coupling layers-one of which would alone hamper synchronization and the other would foster it-reverse their roles when used in a multilayer network. We also analytically demonstrate that increasing the size of a globally coupled layer, that in isolation would induce stable synchronization, makes the multilayer network unsynchronizable.

Network Analysis of Price Comovements Among Corn Futures and Cash Prices

Abstract Due to significant implications for resource and food sectors that directly influence social well-being, commodity price comovements represent an important issue in agricultural economics. In this study, we approach this issue by concentrating on daily prices of the corn futures market and 496 cash markets from 16 states in the United States for the period of July 2006 – February 2011 through correlation based hierarchical analysis and synchronization analysis, which allow for determining interactions and interdependence among these prices, heterogeneities in price synchronization, and their changing patterns over time. As the first study of the issue focusing on prices of the futures and hundreds of spatially dispersed cash markets for a commodity of indubitable economic significance, empirical findings show that the degree of comovements is generally higher after March 2008 but no persistent increase is observed. Different groups of cash markets are identified, each of which has its members exhibit relatively stable price synchronization over time that is generally at a higher level than the synchronization among the futures and all of the 496 cash markets. The futures is not found to show stable price synchronization with any cash market. Certain cash markets have potential of serving as cash price leaders. Results here benefit resource and food policy analysis and design for economic welfare. The empirical framework has potential of being adapted to network analysis of prices of different commodities.

Effect of higher-order interactions on synchronization of neuron models with electromagnetic induction

Recent studies have shown that higher-order interactions have a vital role in exploring the collective dynamics of the networks. In particular, the collective behavior of a network of neuron models with many-body interactions has received much attention among researchers in recent times. In this paper, we study the effect of higher-order interactions in the synchronization stability of the network of neuron models, namely Hindmarsh-Rose and Morris-Lecar models, with electromagnetic induction. We consider both two-body and three-body interactions to be diffusive and analyze their effect on the synchronization of the network of neurons. Our analysis shows that higher-order interactions can make the neurons synchrony with the minimal value of first-order coupling strengths in both neuron models. Besides, electromagnetic flux coupling strength also has a significant effect on the synchronization of neurons. In the Hindmarsh-Rose neuron model, the flux coupling demands higher coupling strength in both the first and second-order interactions for the synchronization of neurons. However, the Morris-Lecar neuron model shows a notable distinct effect, where the flux coupling enhances the synchronization of neurons with lesser first and second-order coupling strengths.

Strong cluster synchronization in complex semiconductor laser networks with time delay signature suppression.

Cluster synchronization is a state where clusters of nodes inside the network exhibit isochronous synchronization. Here, we present a mechanism to realize the strong cluster synchronization in semiconductor laser (SL) networks with complex topology, where stable cluster synchronization is achieved with decreased correlation between dynamics of different clusters and time delay signature concealment. We elucidate that, with the removal of intra-coupling within clusters, the stability of cluster synchronization could be enhanced effectively, while the statistical correlation among dynamics of each cluster decreases. Moreover, it is demonstrated that the correlation between clusters can be further reduced with the introduction of dual-path injection and frequency detuning. The robustness of strong cluster synchronization on operation parameters is discussed systematically. Time delay signature in chaotic outputs of SL network is concealed simultaneously with heterogeneous inter-coupling among different clusters. Our results suggest a new approach to control the cluster synchronization in complex SL networks and may potentially lead to new network solutions for communication schemes and encryption key distribution.

Collective behaviors in a multiple functional network with hybrid synapses

Because of functional differentiation of biological neurons, more functional regions have been developed and formed in the brain and the neurons with the same biophysical function are connected in a specific region. Many neural circuits can be improved to exit specific functions by incorporating special electric components into the branch circuits, and they can be connected to simulate the cooperation of neurons with different biophysical properties. In this paper, three kinds of functional neural circuits are connected to develop a functional network for detecting external illumination, temperature changes and acoustic wave synchronously. The synchronous stability between neurons are much dependent on the intrinsic properties of the synaptic connection along the coupling channels. Electric synapse connection, capacitor-connection and induction coil connection are applied to trigger voltage, electric field and magnetic field couplings along the links in the neural network, respectively. Indeed, the field coupling induced by capacitive and inductive coupling can be controllable under external field by injecting energy continuously. The results indicate that the phase lock of the neural network can be stabilized by taming the coupling intensity carefully, and it can be further enhanced and switched by involving the noise. The Hamilton energy is estimated and in line with the phase synchronization. These results are helpful to know potential biophysical mechanism of synchronous firing and mode selection in the functional network.

Suggesting Hybrid HB and Three-Quarter-Bridge MMC-Based HVDC Systems: Protection and Synchronous Stability Under DC Faults

The HVDC systems have been employing modular multilevel converters (MMC) due to their unique high voltage high power potential. However, the lack of fault ride-through capability imposes restrictions on MMCs that are based on half-bridge (HB) modules. Since it is necessary to limit the fault currents to protect MMCs from serious short circuit faults against pole-to-pole DC fault, several protection schemes have been introduced to deal with the DC short circuit faults. This paper proposes a new hybrid MMC protective topology consisting of a combination of the HB and three-quarter-bridge (TQB) modules. The TQB behaves like an HB under normal operation and has low power losses compared to other protective topologies. Modulation and control of this configuration are like HB-based MMC. In the proposed hybrid protective topology, during a pole to pole DC fault, the fault current can be either blocked or be limited by TQB-SMs. Both simulations and experiments were performed to verify the operation of the suggested hybrid MMC in different modes of operation.

A Real-Time Enhanced Thevenin Equivalent Parameter Estimation Method for PLL Synchronization Stability Control in VSC

The real-time estimation of the AC power system equivalent parameters enables the grid-connected Voltage Source Converter (VSC) to achieve more effective stability control during a short-circuit fault. In this paper, a novel Thevenin Equivalent (TE) parameter estimation method based on local synchronous Phasor Measurement Units (PMUs) is proposed and applied to the Phase-Locked Loop (PLL) synchronization stability control of VSC. First, the relationship between the variation of the measured voltage and the error of the estimated impedance is strictly derived based on the rules of norm inequality. Then, according to the analysis of the upper bound of the system voltage change, a voltage threshold is proposed to select the PMU measurements to ensure the accuracy of the estimation during the large disturbance. Finally, using the estimated TE parameters, the current control instruction of VSC during the fault is calculated in real-time to ensure a synchronous and stable operation. The simulations reveal that the proposed estimation method can accurately track the TE parameters after a fault. Furthermore, the associated current control actions during a fault can ensure the PLL synchronization stability of VSC.

The efficiency evaluation of the power plants turbines control to optimize the agro-industrial complex objects power supply

Modern food systems are entering a fundamentally new stage of technological development, which is based, first of all, on the introduction of new innovative technologies that make increased demands on the energy supply of agricultural enterprises. These requirements are based on ensuring a reliable, efficient and optimal energy supply to agricultural facilities. The article discusses the influence of weight coefficients in the criterion of the quality of optimal control of a complex power system, providing synchronous dynamic stability in the power supply systems of the agro-industrial complex.

Stabilized Time Transfer via a 1000-km Optical Fiber Link Using High-Precision Delay Compensation System

Variations in optical fiber length and refractive index are induced by environmental perturbation, resulting in an additional dynamic propagation delay in fiber-based time synchronization systems, which deteriorate their transfer stability. This disadvantage can be significantly reduced by transmitting the time signal in both directions through fiber and constructing a feedback loop to compensate the propagation delay at the remote end of the link. This paper proposes an analog-digital hybrid proportional integral derivative (PID) control compensation system based on the time-frequency phase-locked loop (TF-PLL). The system is designed to keep the merits of wide servo bandwidth, servo accuracy, and a large dynamic delay compensation range up to 1 s, which is much greater than that reported in previous studies. For proving the validity of this proposed scheme, a self-developed optical fiber time synchronization equipment based on the delay compensation system is applied. The delay compensation system is used on a 1100-km long laboratory optical fiber, and the results show that the time synchronization stability in terms of time deviation (TDEV) is less than 5.92 ps/1 s and 2.56 ps/10,000 s. After successful laboratory evaluation, the proposed system is installed on a real 988.48-km line between the Xi’an Lintong branch of the National Time Service Center (NTSC) and Linfen City, Shanxi Province, realizing the time synchronization of 10 stations along the optical fiber link. The experimental results in the 988.48-km link illustrate that the measured time difference with a peak-to-peak value of 176 ps, the standard deviation of 19.3 ps, and a TDEV of less than 10.49 ps/1 s and 2.31 ps/40,000 s is achieved. The high-precision time delay compensation system proposed in this paper is simple, reliable, and accurate; has a wide range of compensation; and opens up a feasible scheme for providing synchronized time signals to multiple users over the long-distance field optical fiber networks.

Enhancement of visuomotor synchronization by a regular pattern of stimulus presentation

Stable synchronization with external auditory/visual events is important for cooperative behavior, such as playing music in an orchestra. One way to enhance synchronization in the auditory domain is by inserting different tones between tones to synchronize. Synchronized tapping for every other tone or more (1: n tapping) is less variable than that for each tone (1:1 tapping). This phenomenon is called the “subdivision benefit,” which is interpreted as that additional temporal references by subdivided tones make synchronization more stable. However, it is unclear whether visuomotor synchronization becomes more stable by subdividing a stimulus sequence. To clarify this, the present study compared 1:3 tapping with a sequence of three-picture patterns and 1:1 tapping with a single picture repetition. When the inter-tap interval (ITI) was 1200 ms or more, the tapping variability showed a subdivision benefit, irrespective of the position of the pictures (1st, 2nd, or 3rd picture) in the three-picture pattern. However, when the ITI was <1000 ms, subdivision did not have any significant effect. These results imply that the subdivision benefit is due to the additional temporal reference provided by the subdivided stimuli, and the benefit depends on the ITI length.

Cascading Synchronization Instability in Multi-VSC Grid-Connected System

In this letter, a cascading synchronization instability phenomenon is reported in a multi-voltage-source-converter (VSC) grid. By adopting the equal area criterion, it is revealed that during the fault transient, there is static interaction that increases equivalent mechanical power for the original stable-operating VSC. Due to the fast power angle swing of the unstable VSC, there is nonnegligible dynamic interaction, which may decrease its synchronization stability margin. The effect of system parameters on synchronization stability is studied, and the simulation and experimental results verify the analysis.