Showing papers on "Transfer function published in 2019"

Harmonic Stability in Power Electronic-Based Power Systems: Concept, Modeling, and Analysis

Abstract: The large-scale integration of power electronic-based systems poses new challenges to the stability and power quality of modern power grids. The wide timescale and frequency-coupling dynamics of electronic power converters tend to bring in harmonic instability in the form of resonances or abnormal harmonics in a wide frequency range. This paper provides a systematic analysis of harmonic stability in the future power-electronic-based power systems. The basic concept and phenomena of harmonic stability are elaborated first. It is pointed out that the harmonic stability is a breed of small-signal stability problems, featuring the waveform distortions at the frequencies above and below the fundamental frequency of the system. The linearized models of converters and system analysis methods are then discussed. It reveals that the linearized models of ac–dc converters can be generalized to the harmonic transfer function, which is mathematically derived from linear time-periodic system theory. Lastly, future challenges on the system modeling and analysis of harmonic stability in large-scale power electronic based power grids are summarized.

An all-optical neuron with sigmoid activation function.

Abstract: We present an all-optical neuron that utilizes a logistic sigmoid activation function, using a Wavelength-Division Multiplexing (WDM) input & weighting scheme. The activation function is realized by means of a deeply-saturated differentially-biased Semiconductor Optical Amplifier-Mach-Zehnder Interferometer (SOA-MZI) followed by a SOA-Cross-Gain-Modulation (XGM) gate. Its transfer function is both experimentally and theoretically analyzed, showing excellent agreement between theory and experiment and an almost perfect fitting with a logistic sigmoid function. The optical sigmoid transfer function is then exploited in the experimental demonstration of a photonic neuron, demonstrating successful thresholding over a 100psec-long pulse sequence with 4 different weighted-and-summed power levels.

Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

Abstract: This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-...

Feedback Control in Systems Biology

Abstract: Introduction What is feedback control? Feedback control in biological systems Application of control theory to biological systems: a historical perspective References Linear systems Introduction State-space models Linear time-invariant systems and the frequency response Fourier analysis Transfer functions and the Laplace transform Stability Change of state variables and canonical representations Characterising system dynamics in the time domain Characterising system dynamics in the frequency domain Block diagram representations of interconnected systems Case Study I: Characterising the frequency dependence of osmo-adaptation in Saccharomyces cerevisiae Case Study II: Characterising the dynamics of the Dictyostelium external signal receptor network References Nonlinear systems Introduction Equilibrium points Linearisation around equilibrium points Stability and regions of attractions Optimisation methods for nonlinear systems Case study III: Stability analysis of tumor dormancy equilibrium Case study IV: Global optimisation of a model of the tryptophan control system against multiple experiment data References Negative feedback systems Introduction Stability of negative feedback systems Performance of negative feedback systems Fundamental tradeoffs with negative feedback Case Study V: Analysis of stability and oscillations in the p53-Mdm2 feedback system Case Study VI: Perfect adaptation via integral feedback control in bacterial chemotaxis References Positive feedback systems Introduction Bifurcations, bistability and limit cycles Monotone systems Chemical reaction network theory Case Study VII: Positive feedback leads to multistability, bifurcations and hysteresis in a MAPK cascade Case Study VIII: Coupled positive and negative feedback loops in the yeast galactose pathway References Model validation using robustness analysis Introduction Robustness analysis tools for model validation New robustness analysis tools for biological systems Case Study IX: Validating models of cAMP oscillations in aggregating Dictyostelium cells Case Study X: Validating models of the p53-Mdm2 System References Reverse engineering biomolecular networks Introduction Inferring network interactions using linear models Least squares Exploiting prior knowledge Dealing with measurement noise Exploiting time-varying models Case Study XI: Inferring regulatory interactions in the innate immune system from noisy measurements Case Study XII: Reverse engineering a cell cycle regulatory subnetwork of Saccharomyces cerevisiae from experimental microarray data References Stochastic effects in biological control systems Introduction Stochastic modelling and simulation A framework for analysing the effect of stochastic noise on stability Case Study XIII: Stochastic effects on the stability of cAMP oscillations in aggregating Dictyostelium cells Case Study XIV: Stochastic effects on the robustness of cAMP oscillations in aggregating Dictyostelium cells References Index

Analytical fractional PID controller design based on Bode's ideal transfer function plus time delay.

Abstract: In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode's ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.

Generalized Single-Phase Harmonic State Space Modeling of the Modular Multilevel Converter With Zero-Sequence Voltage Compensation

Abstract: The modular multilevel converter (MMC) has attracted extensive research in recent years. An appropriate model is necessary to analyze stability or to design MMC controllers. Several published MMC models have been derived in single-phase form to simplify the modeling mathematics. However, little attention is given to the zero-sequence voltage, which introduces coupling in the single-phase model and leads to significant error. In this paper, after revealing the mechanism behind the zero-sequence voltage, a more accurate generalized single-phase MMC model is proposed, which eliminates the zero-sequence voltage coupling effect and is linearized based on harmonic state space (HSS) theory to precisely characterize the internal harmonic features of MMC. A systematic HSS modeling process is presented for both open-loop and closed-loop conditions. And the proposed model is generalized as it can incorporate different control strategy by controller transfer function substitution. Hence it is valuable to analyze MMC stability and dynamics. Model effectiveness is verified by simulation results.

SISO Transfer Functions for Stability Analysis of Grid-Connected Voltage-Source Converters

Abstract: Converter-grid interaction is of great interest in a weak-grid condition. This paper presents a single-input–single-output (SISO) open-loop transfer function for the stability analysis of grid-connected voltage-source converters. Differing from the conventional input impedance method and the eigenvalue analysis, an alternative multi-input–multi-output closed-loop system is developed in the paper and it eventually yields an SISO open-loop transfer function. This enables the application of a single Nyquist curve for analyzing the overall system stability. The model is validated against time-domain simulations as well as experimental results showing excellent accuracy for predicting the system stability.

Decomposition and Synthesis of High-Order Compensated Inductive Power Transfer Systems for Improved Output Controllability

Abstract: High-order compensation provides more design freedom for inductive power transfer systems and can help improve output voltage/current controllability. This paper develops a simplified decomposition and synthesis method for high-order-compensated inductive power transfer systems. It can achieve load-independent (LI) output under coupling variation, and easily fulfill the various charging requirements, such as constant voltage or constant current. The coupling independent resonance is ensured by using the induced source model, and the whole resonant tank is effectively decomposed as three parts. The power transfer characteristics are discussed for each part, and the requirements for LI output and zero phase angle (ZPA) operation are combined to generate the compensation candidates for both sides. Two families of topologies are synthesized for four kinds of conversions, i.e., voltage to voltage, voltage to current, current to voltage, and current to current. Meanwhile, the proposed method dramatically simplifies the evaluation for the influence of the coil equivalent series resistors on the transfer function and efficiency. These resistor-caused effects are quite different for two families of topologies. Finally, a 6.78-MHz system with 10-W output is designed to verify the difference between two-family topologies.

Aggregation Frequency Response Modeling for Wind Power Plants With Primary Frequency Regulation Service

Abstract: High-penetration wind power access to grid requires wind turbine generator (WTG) to provide frequency regulation service. Consequently, the frequency dynamics of wind power plants (WPPs) integrated system are changing; thus, it is necessary to investigate the dynamic frequency response of WPPs. In this paper, an analytical approach for an aggregated frequency response model for WPPs with primary frequency regulation service is presented and validated. First, different operation region of WTGs is fully taken into account, and a low-order wind power frequency response (WPFR) model with combined frequency control is deduced based on small signal analysis theory, which has been given in the form of symbolic transfer function. Afterwards, a system identification (SI) analytical method is proposed to aggregate a multi-machine WPFR model with heterogeneous parameters into a single equivalent model, which is called an aggregated WPFR (AWPFR) model, and this aggregation method is validated by the mathematical proof. Finally, the accuracy and effectiveness of the AWPFR model is verified through comparisons of simulation results obtained from the multi-machine WPFR model, detailed wind power plant (WPP) model and individual WPFR models, and the impact of the WTG parameters on the system frequency characteristics is analyzed and discussed. Such an aggregation model can provide a convenient way to describe the dynamic frequency response of WPPs by avoiding the need for modeling complex transient processes while maintaining a satisfactory level of accuracy.

Low-Order Response Modeling for Wind Farm-MTDC Participating in Primary Frequency Controls

Abstract: A low-order and system-level response model for wind farms (WFs) and voltage source converter based high-voltage direct current (VSC-HVDC) participating in primary frequency regulation using virtual synchronous machine (VSM) control is developed and validated. The VSM control with virtual power system stabilizer (PSS) function is presented being applicable to all multi-terminal HVDC (MTDC) VSCs. In this context, a general low-order response model (LRM) for presenting the WF-MTDC participating in the frequency control of main AC system is readily established. This modeling method derives transfer function based block diagram offering an illustrative insight into dynamic interaction between AC frequencies and DC voltages. Such a model can also provide a convenient way performing control system designing and parameter tuning. As a paradigm, LRM-based linear quadratic regulation optimization is applied to obtain the droop and damping gains for feasible frequency regulation. The effectiveness of the LRM method is verified through comparisons of the simulation results obtained from different models, controller designs, and parameter tuning approaches, which are all performed on a five-terminal VSC-HVDC connecting WF-side and main AC systems.

Analysis of virtual synchronous generator control and its response based on transfer functions

Abstract: Virtual Synchronous Generator (VSG) control has been proposed as a means to control power electronics converter interfaced generation and storage which retains the dynamics of the conventional synchronous machine. This study provides a comprehensive, transfer function based, analysis of VGS control, which can be used as the basis for the design of VSG transient and steady-state performance. Based on a hardware validated, large signal model, a small signal model and associated transfer functions which describe the changes in real and reactive powers in response to changes in references and grid frequency disturbances. The derived transfer functions are used to obtain insight into the correct design of VSG controllers. The small signal models, transfer functions and associated analysis are validated by comparison with measured results on a scaled hardware system.

A New Error Estimator for Reduced-Order Modeling of Linear Parametric Systems

Abstract: Efficient error estimation is important for reliable reduced-order modeling with guaranteed accuracy. We propose an error estimator for reduced-order modeling of linear parametric dynamical systems. The error estimator estimates the error of the reduced transfer function in the frequency domain and can be easily extended to the output error estimation of the reduced-order models (ROMs) for linear steady parametric systems. It is tight and cheap to compute. Using the error estimator, the ROM can be adaptively obtained with high reliability. Numerical results show that the error estimator can accurately estimate the true error even for transfer functions with many resonances. Compared with an existing error bound, the proposed error estimator can be orders of magnitudes sharper and needs much less computational time.

Role of modern fractional derivatives in an armature-controlled DC servomotor

Abstract: This paper deals with the comparative analysis of modern fractional techniques for an armature-controlled DC servomotor. The mathematical modeling of an armature-controlled DC servomotor is based on the angular displacement of the motor shaft and the armature current in ampere. The governing linear differential equations are fractionalized in terms of Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional differentiations in the ranges $ 0\leq\xi_{1} \leq 1$ and $ 0\leq\xi_{2}\leq 1$, respectively. The fractional ordinary differential equations have been solved by implementing Laplace transform techniques. The transfer function of an armature-controlled DC servomotor is obtained by the coupling of fractional ordinary differential equations. The calculations of transfer functions have been traced out through the Mathcad 15 software while graphical simulation is based on MATLAB. In order to control the systems’ behavior, the transfer function is depicted graphically for fractional and non-fractional solutions along with embedded parameters. Our results suggest that the speed of rotation relies on the voltage which precisely controls the angular position of servomechanism through both types of fractional differentiation.

Reset control approximates complex order transfer functions

Abstract: A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in the literature are unsatisfactory for several reasons: the desired behaviour of the gain may be difficult or impossible to obtain, or non-minimum phase zeros may appear, or even unstable open-loop poles. We propose an alternative nonlinear approximation, combining a CRONE approximation of a fractional derivative with reset control, which does not suffer from these problems. An experimental proof of concept confirms the good results of this approximation and shows that nonlinear effects do not preclude the desired performance.

Parameters identification and trajectory control for a hydraulic system.

Abstract: In order to improve the tracking accuracy of a hydraulic system, an improved ant colony optimization algorithm (IACO) is proposed to optimize the values of proportional-integral-derivative (PID) controller. In addition, this paper presents an experimental study on the parameters identification to deduce accurate numerical values of the hydraulic system, which also determines the relationship between control signal and output displacement. Firstly, the basic principle of the hydraulic system and the mathematical model of the electro-hydraulic proportional control system are analyzed. Based on the theoretical models, the transfer function of the control system is obtained by recursive least square identification method (RLS). Then, the key parameters of the control system model are obtained. Some improvements are proposed to avoid premature convergence and slow convergence rate of ACO: the transition probability is revised based adjacent search mechanism, dynamic pheromone evaporation coefficient adjustment strategy is adopted, pheromone update rule and parameters optimization range are also improved. Then the proposed IACO tuning based PID controller and the identification parameters are modeled and simulated using MATLAB/Simulink and AMESim co-simulation platform. Comparisons of IACO, standard ACO and Ziegler-Nichols (Z-N)PID controllers are carried out with different references as step signal and sinusoidal wave using the co-simulation platform. The simulation results of the bucket system using the proposed controller demonstrates improved settling time, rise time and the convergence speed with a new objective function J. Finally, experiments with leveling operations are performed on a 23 ton robotic excavator. The experimental results show that the proposed controller improves the trajectory accuracy of the leveling operation by 28% in comparison to the standard ACO-PID controller.

A Unified Frequency-Domain Model for Automatic Generation Control Assessment Under Wind Power Uncertainty

Abstract: High frequency uncertainty of wind power is highly stochastic and unpredictable. It can have considerable impacts on automatic generation control (AGC) for power systems. This paper proposes a novel frequency-domain model to evaluate AGC performances under wind power uncertainty in frequency domain. High frequency volatilities are accurately described by the frequency model of wide-sense stationary stochastic process. The newly introduced frequency tools enable the variations of power/energy units and network variables to be represented by the generalized transfer functions of the independent or joint stochastic processes of wind power fluctuations. The time-domain operation constraints and performance criteria of CPS1 and CPS2 are successfully transformed into frequency domain on basis of a theorem and its corollary related to the calculation of cross correlation functions proved in this paper. In general, this paper proposes a unified way of modeling volatility sources, system operations, and AGC performance assessments in frequency domain. Case studies on an isolated system and IEEE 118 interconnected system demonstrate the effectiveness and the conveniences of the proposed frequency domain model.

A robust force feed-forward observer for an electro-hydraulic control loading system in flight simulators.

Abstract: A robust feed-forward observer is proposed for feel force control of an electro-hydraulic control loading system in flight simulators. Combining a velocity feed-forward compensator, the proposed control structure can effectively reduce a disturbance force caused by the control displacement of a pilot to further improve control performances. The electro-hydraulic control loading system is described as a force–displacement impedance system, including a mechanical system and a hydraulic control system, and its dynamic model is established as a double-loop system. Implementation of the proposed controller includes observer model design and filter optimization. Aiming at a force closed-loop which is always a non-minimum-phase system, an effective design method of an approximated inverse model is presented for obtaining an observer model, and it is an biregular transfer function. With the particular observer model, an optimization for the filter of feed-forward observer structure is carried out, by transforming the original structure into a control structure with consideration of modeling error between the obtained observer model and the actual inverse model, which is a 2-independent-controllers structure. Then, an H ∞ controller is employed to optimize the transformed structure to indirectly obtain an optimized filter. In order to ensure existence of the H ∞ controller for the transformed structure of the feed-forward observer with a biregular observer model, some dynamic characteristics are analyzed and proved. Based on the characteristics, a nominal model modification method is presented to obtain a well-posed H ∞ control structure. For designing a performance weighting function, an optimize goal is discussed and its proof is given, and then an algorithm using a bisection method is proposed to further improve the robust performance of the proposed controller. To verify the efficiency of the proposed controller, control performances of the electro-hydraulic control loading system are evaluated in experiments and are compared with those of other controllers, including the proportional–integral–derivative controller, the velocity feed-forward compensator, and the H ∞ controller. Experimental results show that the proposed controller can effectively reduce the disturbance force of the electro-hydraulic control loading system, and its impedance characteristics are closer to the ideal force feel model than the other controllers.

Alternating Direction Method of Multipliers (ADMMs) Based Distributed Approach For Wide-Area Control

Abstract: In this paper, an alternating direction method of multipliers based novel distributed wide-area control architecture is proposed for damping the interarea oscillations. In this approach, first, an interconnected power system is divided into areas based on coherency grouping. Second, local processors are assigned on each area that estimate a black-box transfer function model based on Lagrange multipliers using measurements. These local area processors are then used to estimate a global transfer function model of the power system based on a consensus algorithm through a global processor. After convergence, a transfer function residue corresponding to the interarea mode of interest is derived, to determine optimal wide area control loop. Finally, a wide-area damping controller is designed based on this information. The efficacy of the controller is validated using two area and IEEE-39 bus test systems on RTDS/RSCAD and MATLAB cosimulation platform.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones—Part I: Spatiotemporal Transfer Function and Graphical Guide

Abstract: The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent “effective” sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Polarimetric Wireless Indoor Channel Modeling Based on Propagation Graph

Abstract: This paper generalizes a propagation graph model to polarized indoor wireless channels. In the original contribution, the channel is modeled as a propagation graph in which vertices represent transmitters, receivers, and scatterers, while edges represent the propagation conditions between vertices. Each edge is characterized by an edge transfer function accounting for the attenuation, delay spread, and the phase shift on the edge. In this contribution, we extend this modeling formalism to polarized channels by incorporating depolarization effects into the edge transfer functions and hence, the channel transfer matrix. We derive closed form expressions for the polarimetric power delay spectrum and cross-polarization ratio of the indoor channel. The expressions are derived considering average signal propagation in a graph and relate these statistics to model parameters, thereby providing a useful approach to investigate the averaged effect of these parameters on the channel statistics. Furthermore, we present a procedure for calibrating the model based on method of moments. Simulations were performed to validate the proposed model and the derived approximate expressions using both synthetic data and channel measurements at 15 GHz and 60 GHz. We observe that the model and approximate expressions provide good fit to the measurement data.

Generalized predictor based active disturbance rejection control for non-minimum phase systems.

Abstract: In this paper, a generalized predictor based control scheme is proposed to improve system performance of set-point tracking and disturbance rejection for non-minimum phase (NMP) systems. By using a generalized predictor to estimate the system output without time delay, a model-based extended state observer (MESO) is designed to simultaneously estimate the system state and disturbance. Accordingly, an active disturbance rejection control design is developed which consists of a state feedback control and a feedforward control for the disturbance rejection. The MESO and feedback controllers are analytically derived by specifying the desired characteristic roots of MESO and closed-loop system poles, respectively. To improve the output tracking performance, a pre-filter is designed based on a desired closed-loop transfer function for the set-point tracking. A sufficient condition guaranteeing robust stability of the closed-loop system against time-varying uncertainties is established in terms of linear matrix inequalities (LMIs). Three illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control scheme.

Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function

Abstract: Author(s): Zhou, Q; Oldenburg, CM; Rutqvist, J | Abstract: Numerous analytical solutions have been developed for modeling thermal perturbations to underground formations caused by deep-well injection of fluids. Each solution has been derived for a specific boundary value problem and a simplified flow network with one set of parallel fractures. In this paper, new generalized solutions G*(x, s) are developed using (existing) global transfer functionsG*0 (x,s) and a new memory function g*(s), where x and s are the space and Laplace variable. The memory function represents the solutions of conductive heat exchange between fractures and matrix blocks and between fractured aquifers and unfractured aquitards. The memory function is developed to account for multirate exchange induced by different shapes, sizes, properties, and volumetric fractions of matrix blocks bounded by multiple sets of orthogonal fractures with different spacing. The global transfer functions represent the fundamental solutions to convective, convective-conductive, and convective-dispersive heat transport in fractures (or aquifers) without exchange and are available for various (1-D linear, 1-D radial, 2-D dipole, and single-well injection-withdrawal) flow fields. The new solutionswith exchange are developed usingG*(x,s) = B*(s)G*0{x, s[1 + Θg*(s)]}, thereby greatly simplifying solution development in a novel way, where Θ and B*(s) are a fracture-matrix scaling factor and the boundary condition function. The new solutions are applied to several example problems, showing that heat transport in fractured aquifers is significantly impacted by (1) thermal dispersion in fractures that is rarely considered, (2) multirate heat exchange with a wide range of size and anisotropy of rectangular matrix blocks, and (3) heat exchange between aquifers and aquitards.

Lyapunov Energy Function Based Control Method for Three-Phase UPS Inverters With Output Voltage Feedback Loops

Abstract: In this study, a Lyapunov energy function based control method with output voltage feedback loops is proposed for three-phase uninterruptible power supply (UPS) inverters. The presented paper demonstrates that the traditional Lyapunov-energy-function-based control method not only leads to considerable steady-state error in the output voltage, but also distorts the output voltage waveforms. Therefore, a modification has been performed on the traditional Lyapunov-energy-function-based control by incorporating the output voltage feedback loops in the control variables. The robustness of the proposed control method has been studied analytically through transfer functions which are expressed as the ratio of the output voltage to its reference. These analytical results are validated experimentally. In addition, the steady-state and dynamic performances of the proposed control method are also tested experimentally on a three-phase UPS inverter operating with linear (resistive) and nonlinear (diode-bridge rectifier) loads. As a consequence of incorporating output voltage feedback loops into the control variables, the proposed control method offers strong robustness against variations in LC filter parameters, high-quality sinusoidal output voltage along with acceptable total harmonic distortion (THD) values under linear and nonlinear loads, fast dynamic response under abrupt load changes, and negligibly small steady-state error in the output voltage.

Regenerative properties of the linear hawkes process with unbounded memory

Abstract: We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit independence in the Poisson cluster point process decomposition, and the regeneration times are not stopping times for the Hawkes process. The regeneration time is interpreted as the renewal time at zero of a M/G/infinity queue, which yields a formula for its Laplace transform. When the transfer function admits some exponential moments, we stochastically dominate the cluster length by exponential random variables with parameters expressed in terms of these moments. This yields explicit bounds on the Laplace transform of the regeneration time in terms of simple integrals or special functions yielding an explicit negative upper-bound on its abscissa of convergence. These regenerative results allow, e.g., to systematically derive long-time asymptotic results in view of statistical applications. This is illustrated on a concentration inequality previously obtained with coauthors.

A robust control strategy to improve transient stability for AC-DC interconnected power system with wind farms

Abstract: In view of the variable parameters that affect the transient stability of electromagnetic torque and mechanical torque balance in AC-DC system, and the uncertainty of wind power in large-scale interconnection of wind farm. This paper proposes a linear parameter varying (LPV) robust feedback control method for transient stability of interconnected systems. The proposed LPV robust feedback control method uses the DC channel power control and the mechanical power in the interconnected system as the control target to improve the transient stability of the interconnected system with wind farm channel. Firstly, aiming at the strong nonlinear characteristics of the interconnected system, the power balance and the wind power output uncertainty in the transient process, the transient process is designed as a linear model of variable parameters. Then, the H∞ robust output feedback controller is designed according to the LPV model. The transient stability control strategy topology and transfer function of the interconnected system are proposed. Finally, the proposed scheme is verified by an interconnected system formed by four equal-value grids through AC and DC lines in a digital simulation platform. The results show that the LPV robust feedback control model proposed in this paper has better response characteristics and transient stability control effects for interconnected systems with wind power weak sending-end system.