Transient Damping of Virtual Synchronous Generator for Enhancing Synchronization Stability during Voltage Dips

Virtual synchronous generators(VSGs)are widely introduced to the renewable power generation,the variablespeed pumped storage units,and so on,as a promising gridforming solution.It is noted that VSGs can provide virtual inertia for frequency support,but the larger inertia would worsen the synchronization stability,referring to keeping synchronization with the grid during voltage dips.Thus,this paper presents a transient damping method of VSGs for enhancing the synchronization stability during voltage dips.It is revealed that the loss of synchronization(LOS)of VSGs always accompanies with the positive frequency deviation and the damping is the key factor to remove LOS when the equilibrium point exists.In order to enhance synchronization stability during voltage dips,the transient damping is proposed,which is generated by the frequency deviation in active power loop.Additionally,the proposed method can realize seamless switching between normal state and grid fault.Moreover,detailed control design for transient damping gain is given to ensure the synchronization stability under different inertia requirements during voltage dips.Finally,the experimental results are presented to validate the analysis and the effectiveness of the improved transient damping method.

Modeling and small-signal stability analysis of doubly-fed induction generator integrated system

Owing to their stability,doubly-fed induction generator(DFIG)integrated systems have gained considerable interest and are the most widely implemented type of wind turbines and due to the increasing escalation of the wind generation penetration rate in power systems.In this study,we investigate a DFIG integrated system comprising four modules:(1)a wind turbine that considers the maximum power point tracking and pitch-angle control,(2)induction generator,(3)rotor/grid-side converter with the corresponding control strategy,and(4)AC power grid.The detailed small-signal modeling of the entire system is performed by linearizing the dynamic characteristic equation at the steady-state value.Furthermore,a dichotomy method is proposed based on the maximum eigenvalue real part function to obtain the critical value of the parameters.Root-locus analysis is employed to analyze the impact of changes in the phase-locked loop,short-circuit ratio,and blade inertia on the system stability.Lastly,the accuracy of the small-signal model and the real and imaginary parts of the calculated dominant poles in the theoretical analysis are verified using PSCAD/EMTDC.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Transient Stability Assessment of Synchronous Generator in Power System with High-Penetration Photovoltaics

As photovoltaic （PV） capacity in power system increases, the capacity of synchronous generator needs to be reduced relatively. This leads to the lower system inertia and the higher generator reactance, and hence the generator transient stability may negatively be affected. In particular, the impact on the transient stability may become more serious when the considerable amounts of PV systems are disconnected simultaneously during voltage sag. In this work, the generator transient stability in the power system with significant PV penetration is assessed by a numerical simulation. In order to assess the impact from various angles, simulation parameters such as levels of PV penetration, variety of power sources （inverter or rotational machine）, and existence of LVRT capability are considered. The simulation is performed by using PSCAD/EMTDC software.

Tuning method for governor control parameters of hydropower generator in isolated grid considering primary frequency performance and small-signal stability

This paper presents a method of tuning governor control parameters of an isolated hydropower generator considering the primary frequency performance and small-signal stability. First, generators that can be operated in isolated state are identified. Second, different schemes are proposed for generator mode switching from on-grid to off-grid state through comparison and mechanism analysis. Third, the time domain model and frequency domain model of the isolated generator governor are constructed to respectively estimate the primary frequency performance and small signal stability. Parameter sets that satisfy the primary frequency performance and small signal stability are acquired as optimal values of governor control parameters. Finally, the measurement-based parameters of the governor are identified and validated using simulations to demonstrate the feasibility and effectiveness of the method.

Small-Signal Stability Analysis of Wind Power System Based on DFIG

This paper focuses on the small-signal stability of power system integrated with DFIG-based wind farm. The model of DFIG for small-signal stability analysis has built;the 3-generator 9-bus WECC test system is modified to investigate the impacts of large scale integration of wind power on power system small-signal stability. Different oscillatory modes are obtained with their eigenvalue, frequency and damping ratio, the results from eigenvalue analysis are presented to demonstrate the small-signal stability of power system is enhanced with the increasing output of the wind farm.

Transient Stability Analysis of Synchronous Generator in Power System with Renewable Power Sources Installed

The impact of large-scale grid-connected renewable power sources, such as wind generators and solar photovoitaic systems, on transient stability of synchronous generators is discussed in this paper. The permanent magnet synchronous generator with variable speed wind turbine is used in the simulation analysis as a wind generator model. The transient stability analysis is performed for IEEE 9-bus system model with high-penetration renewable power sources. The effect of FRT （fault ride-through） capability implemented for each power source on the transient stability is investigated.

Transient Stability Assessment of Synchronous Generator in Power System with High-Penetration Photovoltaics （Part 2）

In the previous paper [1], the transient stability of synchronous generator in power system with high-penetration PV （photovoltaic） was assessed by simulation analysis of a single-machine infinite-bus system model. Through the simulation analysis, we have obtained some conclusions in terms of the impact of high-penetration PV on the stability. However, for more accurate assessment of the transient stability, it is necessary to analyze various simulation models considering many other power system conditions. This paper presents the results of the analysis for the transient stability simulation performed for IEEE 9-bus system model, in which the effects of various conditions, such as variety of power sources （inverter or rotational machine）, load characteristics, existence of LVRT （low-voltage ride-through） capability and fault locations, on the transient stability are investigated.

Asymptotical p-moment stability of stochastic impulsive differential system and its application to chaos synchronization

In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.

Large-disturbance Stability Analysis of Power Systems with Synchronous Generator and Converter-interfaced Generation

This letter studies large-disturbance stability of the power system with a synchronous generator(SG)and a converter-interfaced generation(CIG)connected to infinite bus.The power system is multi-timescale and first simplified.It is shown that the boundary of region of attraction(ROA)of the simplified model is composed of stable manifolds of unstable equilibrium point(UEP)or semi-singular point(SSP),named anchor points,and singular surface pieces.The type of anchor point determines the dominant instability pattern of the power system.When the anchor point is UEP or SSP,the dominant instability pattern is the instability of rotor angle of SG or the instability of phase-locked loop and outer control loop(OCL)of CIG,respectively.Transition of dominant instability pattern can be analyzed with the relative position relationship between UEP and SSP.The effect of OCL is discussed.When the OCL is activated,the ROA becomes smaller and the system is more prone to instability of CIG.It is necessary to consider the OCL when studying the large-disturbance stability of the power system.

Stability analysis of synchronization in discrete-time complex dynamical networks

In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.

Synchronization and Stability of a Nonlinear Vibrating Mechanical System Characterized by Asymmetrical Piecewise Linearity

In previous studies about the synchronization of vibrators,the restoring forces of springs are mainly treated as linear directly,whereas the nonlinear features are rarely considered in vibrating systems.To make up this drawback,a dynamical model of a nonlinear vibrating mechanical system with double rigid frames(RFs),driven by two vibrators,is proposed to explore the synchronization and stability of the system.In this paper,the nonlinearity is reflected in nonlinear restoring forces of springs characterized by asymmetrical piecewise linear,where the nonlinear stiffness of springs is linearized equivalently using the asymptotic method.Based on the average method and Hamilton’s principle,the theory conditions to achieve synchronization and stability of two vibrators are deduced.After the theory analyses,some numerical qualitative analyses are given to reveal the coupling dynamical characteristics of the system and the relative motion properties between two RFs.Besides,some experiments are carried out to examine the validity of the theoretical results and the correctness of the numerical analyses results.Based on the comparisons of the theory,numeric and experiment,the ideal working regions of the system are suggested.Based on the present work,some new types of vibrating equipment,such as vibrating discharging centrifugal dehydrators/conveyers/screens,can be designed.

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.

Small-signal Stability Constrained Optimal Power Flow Considering Eigenvalue Distribution

In the existing small-signal stability constrained optimal power flow(SSSC-OPF)algorithms,only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold,e.g.,damping ratio threshold and real-part threshold of eigenvalue,are considered in the small-signal stability constraints.The effect of steady-state,i.e.,operating point,changes on eigenvalues is not fully taken into account.In this paper,the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane.The small-signal stability constraint is embedded into the standard optimal power flow model for generation reschedul-ing.The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach,while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues.To improve the computation speed,a hybrid algorithm for eigenvalue computation in the optimization process is proposed,which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation.The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.

MEMS Huygens Clock Based on Synchronized Micromechanical Resonators

With the continuous miniaturization of electronic devices,microelectromechanical system(MEMS)oscillators that can be combined with integrated circuits have attracted increasing attention.This study reports a MEMS Huygens clock based on the synchronization principle,comprising two synchronized MEMS oscillators and a frequency compensation system.The MEMS Huygens clock improved shorttime stability,improving the Allan deviation by a factor of 3.73 from 19.3 to 5.17 ppb at 1 s.A frequency compensation system based on the MEMS oscillator’s temperature-frequency characteristics was developed to compensate for the frequency shift of the MEMS Huygens clock by controlling the resonator current.This effectively improved the long-term stability of the oscillator,with the Allan deviation improving by 1.6343105 times to 30.9 ppt at 6000 s.The power consumption for compensating both oscillators simultaneously is only 2.85 mW·℃^(-1).Our comprehensive solution scheme provides a novel and precise engineering solution for achieving high-precision MEMS oscillators and extends synchronization applications in MEMS.

Small-signal Stability Criteria in Power Electronics-dominated Power Systems:A Comparative Review

To tackle emerging power system small-signal stability problems such as wideband oscillations induced by the large-scale integration of renewable energy and power electronics,it is crucial to review and compare existing small-signal stability analysis methods.On this basis,guidance can be provided on determining suitable analysis methods to solve relevant small-signal stability problems in power electronics-dominated power systems(PEDPSs).Various mature methods have been developed to analyze the small-signal stability of PEDPSs,including eigenvalue-based methods,Routh stability criterion,Nyquist/Bode plot based methods,passivity-based methods,positive-net-damping method,lumped impedance-based methods,bifurcation-based methods,etc.In this paper,the application conditions,advantages,and limitations of these criteria in identifying oscillation frequencies and stability margins are reviewed and compared to reveal and explain connections and discrepancies among them.Especially,efforts are devoted to mathematically proving the equivalence between these small-signal stability criteria.Finally,the performance of these criteria is demonstrated and compared in a 4-machine 2-area power system with a wind farm and an IEEE 39-bus power system with 3 wind farms.

Suppression and synchronization of chaos in uncertain time-delay physical system

The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.

Impact of coupling function on stability of synchronization for complex dynamical networks

In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.

Stability Analysis, Chaos Control of Fractional Order Vallis and El-Nino Systems and Their Synchronization

In this article the authors have studied the stability analysis and chaos control of the fractional order Vallis and El-Nino systems. The chaos control of these systems is studied using nonlinear control method with the help of a new lemma for Caputo derivative and Lyapunov stability theory.The synchronization between the systems for different fractional order cases and numerical simulation through graphical plots for different particular cases clearly exhibit that the method is easy to implement and reliable for synchronization of fractional order chaotic systems. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article.