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.

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.

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.

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.

Simplified equivalent models of large-scale wind power and their application on small-signal stability

With the rapid growth of grid-connected wind power penetration level,it is necessary to study the impacts of wind power on power system stability.The small-signal stability of power systems with large-scale wind power is explored using the eigenvalue analysis method.A prototype sample system,the two-synchronous-generator system with a wind farm,is proposed for theoretical analysis.Then,simplified models of wind turbines(WTs)and the corresponding equivalent models of wind farms are analyzed.Three kinds of typical WT models,i.e.,squirrel cage induction generator,doubly-fed induction generator,and permanent magnet synchronous generator are used.Furthermore,based on the simplified equivalent models,effects of large-scale wind farms on the electromechanical oscillation modes(EOMs)of synchronous systems are discussed.Simulation results indicate that wind farms of the three kinds of WTs have positive effects on EOMs.However,long transmission lines connecting wind farmto the systemmay produce negative effects on the small-signal stability of the system.

Coordinated Design and Application of Robust Damping Controllers for Shunt FACTS Devices to Enhance Small-signal Stability of Large-scale Power Systems

This paper presents a robust and coordinated supplementary damping controller design of multiple reactive FACTS controllers and their application in a large-scale power system.Reactive FACTS devices,such as static synchronous compensators(STATCOM)and static VAR compensators(SVC),are considered and assessed for their damping controller design.Control objectives,including regional pole placement and norm bounded mix sensitivities,are used to solve the bilinear matrix inequality(BMI)problems in each linearized model via a two-step method.Multiple damping controllers are sequentially designed to avoid coupling effect among the input signals and increase the reliability of the proposed design.A 5-area 16-machine 68-bus power system is used for the implementation of the damping controllers.Numerical linear analysis and real-time simulations in a test platform based on Real-time digital simulators(RTDS)are adopted to test the feasibility and robustness of the coordinated damping controllers.

A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System

With the rapid development of power-electronicsenabled power systems,the new converter-based generators are deteriorating the small-signal stability of the power system.Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities,its accuracy has not been carefully investigated.Besides,the element-based formulation for computing closed-form eigenvalue sensitivities has not been used in any commercial software due to the average efficiency,complicated formulation,and errorprone characteristics.Based on the matrix calculus,this paper proposes an easily manipulated formulation of the closed-form eigenvalue sensitivities with respect to the power generation.The distinguishing feature of the formulation is that all the formulas consist of vector and matrix operations,which can be performed by developed numerical algorithms to take full advantages of architectural features of the modern computer.The tests on WSCC 3-machine 9-bus system,New England 10-machine 39-bus system,and IEEE 54-machine 118-bus system show that the accuracy of the proposed formulation is superior to the numerical differentiation method and the efficiency is also greatly improved compared to the element-based closed-form formulation.The proposed formulation will be helpful to perform a more accurate and faster stability analysis of a power grid with converter-based devices.

Distributed Control Framework and Scalable Small-signal Stability Analysis for Dynamic Microgrids

As a growing number of microgrids(MGs)has been integrated into the modern power grids,the interconnection and applicable cooperation among multiple MGs motivate the development of networked MGs.Dynamic MGs,as an advanced networked MGs structure,can not only integrate multiple MGs into the distribution system but also fulfill the requested system network reconfiguration with improved flexibility.A general distributed control approach for networked MGs is reviewed.A distributed control framework for dynamic MGs operation is developed,along with an extensible architecture with considerations of large-scale distributed energy resources(DERs)integration.A scalable small-signal stability analysis is conducted per the proposed distributed control strategies and the conditions under which the system is exponentially stable are derived.At last,the effectiveness of the proposed control framework and stability analysis are verified using a 6-bus test feeder.

A matrix-perturbation-theory-based optimal strategy for small-signal stability analysis of large-scale power grid

In this paper,a sensitivity matrix based approach is proposed to improve the minimum damping ratio.The proposed method also avoids burdensome deviation calculations of damping ratio of large-scale power grids when compared to the Small-Signal-Stability Constrained Optimal Power Flow(SSSC-OPF)approach.This is achieved using the Matrix Perturbation Theory(MPT)to deal with the 2nd order sensitivity matrices,and the establishment of an optimal corrective control model to regulate the output power of generating units to improve the minimum damping ratio of power grids.Finally,simulation results on the IEEE 9-bus,IEEE 39-bus and a China 634-bus systems show that the proposed approach can significantly reduce the burden of deviation calculation,while enhancing power system stability and ensuring calculation accuracy.

Small-signal stability analysis of photovoltaic generation connected to weak AC grid

A small-signal model of photovoltaic(PV)generation connected to weak AC grid is established based on a detailed model of the structure and connection of a PV generation system. An eigenvalue analysis is then employed to study the stability of PV generation for different grid strengths and control parameters in a phaselocked loop(PLL) controller in the voltage source converter. The transfer function of the power control loop in the dq rotation frame is developed to reveal the influence mechanism of PLL gains on the small-signal stability of PV generation. The results can be summarized as follows:(1)oscillation phenomena at a frequency of about 5 Hz may occur when the grid strength is low;(2) the tuning control parameters of the PLL have a noticeable effect on the damping characteristics of the system, and larger proportional gain can improve the system damping;(3)within a frequency range of 4-5 Hz,the PLL controller has positive feedback on the power loop of PV generation. A virtual inductance control strategy is proposed to improve the operational stability of PV generation. Finally, a simulation model of PV generation connected to weak AC grid is built in PSCAD/EMTDC and the simulation results are used to validate the analysis.

A novel small-signal equivalent circuit model for GaN HEMTs incorporating a dual-field-plate

An accurate and novel small-signal equivalent circuit model for GaN high-electron-mobility transistors(HEMTs)is proposed,which considers a dual-field-plate(FP)made up of a gate-FP and a source-FP.The equivalent circuit of the overall model is composed of parasitic elements,intrinsic transistors,gate-FP,and source-FP networks.The equivalent circuit of the gate-FP is identical to that of the intrinsic transistor.In order to simplify the complexity of the model,a series combination of a resistor and a capacitor is employed to represent the source-FP.The analytical extraction procedure of the model parameters is presented based on the proposed equivalent circuit.The verification is carried out on a 4×250μm GaN HEMT device with a gate-FP and a source-FP in a 0.45μm technology.Compared with the classic model,the proposed novel small-signal model shows closer agreement with measured S-parameters in the range of 1.0 to 18.0 GHz.

Small-signal Stability Analysis and Improvement with Phase-shift Phase-locked Loop Based on Back Electromotive Force Observer for VSC-HVDC in Weak Grids

Voltage source converter based high-voltage direct current(VSC-HVDC)transmission technology has been extensively employed in power systems with a high penetration of renewable energy resources.However,connecting a voltage source converter(VSC)to an AC weak grid may cause the converter system to become unstable.In this paper,a phase-shift phaselocked loop(PS-PLL)is proposed wherein a back electromotive force(BEMF)observer is added to the conventional phaselocked loop(PLL).The BEMF observer is used to observe the voltage of the infinite grid in the stationaryαβframe,which avoids the problem of inaccurate observations of the grid voltage in the dq frame that are caused by the output phase angle errors of the PLL.The VSC using the PS-PLL can operate as if it is facing a strong grid,thus enhancing the stability of the VSC-HVDC system.The proposed PS-PLL only needs to be properly modified on the basis of a traditional PLL,which makes it easy to implement.In addition,because it is difficult to obtain the exact impedance of the grid,the influence of shortcircuit ratio(SCR)estimation errors on the performance of the PS-PLL is also studied.The effectiveness of the proposed PSPLL is verified by the small-signal stability analysis and timedomain simulation.

Small-Signal Equivalent Circuit Modeling of a Photodetector Chip

A small-signal equivalent circuit model and the ted. The equivalent lumped circuit, which takes the main extraction techniques for photodetector chips are presen- factors that limit a photodetector＇s RF performance into consideration,is first determined based on the device＇s physical structure. The photodetector＇s S parameters are then on-wafer measured, and the measured raw data are processed with further calibration. A genetic algorithm is used to fit the measured data, thereby allowing us to calculate each parameter value of the model. Experimental resuits show that the modeled parameters are well matched to the measurements in a frequency range from 130MHz to 20GHz, and the proposed method is proved feasible. This model can give an exact description of the photodetector chip＇s high frequency performance,which enables an effective circuit-level prediction for photodetector and optoelectronic integrated circuits.

Small-signal modeling and parameter extraction method for a multigate GaAs pHEMT switch

This paper presents an accurate small-signal model for multi-gate GaAs pHEMTs in switching-mode.The extraction method for the proposed model is developed.A 2-gate switch structure is fabricated on a commercial 0.5μm AlGaAs/GaAs pHEMT technology to verify the proposed model.Excellent agreement has been obtained between the measured and simulated results over a wide frequency range.

Small-signal analysis of a rectangular helix structure traveling-wave-tube

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube （TWT） for a solid sheet electron beam. The ＂hot＂ dispersion equation is obtained by means of the self-consistent field theory. The small signal analysis,which includes the effects of the beam parameters and slow-wave structure （SWS） parameters,is carried out by theoretical computation. The numerical results show that the bandwidth and the small-signal gain of the rectangular helix TWT increase as the beam current increases;and the beam voltage not obviously influences the small signal gain. Among different rectangular helix structures,the small-signal gain increases as the width of the rectangular helix SWS increases,however,the bandwidth decreases whether structure parameters a and L or ψ and L are fixed or not.In addition,a comparison of the small-signal gain of this structure with a conventional round helix is made.The presented analysis will be useful for the design of the TWT with a rectangular helix circuit.

A complete small-signal HBT model including AC current crowding effect

An improved small-signal equivalent circuit of HBT concerning the AC current crowding effect is proposed in this paper. AC current crowding effect is modeled as a parallel RC circuit composed of Cbi and Rbi, with distributed base-collector junction capacitance also taken into account. The intrinsic portion is taken as a whole and extracted directly from the measured Sparameters in the whole frequency range of operation without any special test structures. An HBT device with a 2 × 20 μm^(2) emitter-area under three different biases were used to demonstrate the extraction and verify the accuracy of the equivalent circuit.

A Direct Parameter-Extraction Method for GaInP/GaAs Heterojunction Bipolar Transistors Small-Signal Model

An accurate and broad-band method for hetero-junction bipolar transistors(HBT) small-signal model parameters-extraction is presented in this paper. An equivalent circuit forthe HBT under a forward-bias condition is proposed for extraction of accessresistance and parasiticinductance. This method differs from previous ones by extracting the c-quivalent circuit parameterswithout using special test structure or global numerical optimization techniques. The mainadvantage of this method is that a unique and physically meaningful set of intrinsic parameters isextracted from impedance and admittance representation of the measured S-pa-rameters in thefrequency range of 1-12 GHz under different bias conditions. The method yields a deviation of lessthan 5% between measured and modeled S-parameters.

Pressure Dependence of the Small-Signal Gain and Saturation Intensity of a Copper Bromide Laser

A pair of copper bromide lasers in an oscillator–amplifier configuration is used to investigate the small signal gain and saturation intensity as amplifying parameters and output power of lasers, versus pressure of buffer gas. It is shown that the amplifying parameters and laser output power have a maximum value at optimum buffer gas pressure of 11？Torr. The challenge between microscopic parameters such as stimulated emission cross section, laser upper level lifetime, and population inversion, which determine the values of laser characteristics respective to the operational pressure of buffer gas, are investigated. Thus an optimum delay time of about 10？ns is determined, and a maximum output power equivalent to about 12？W is extracted. The amplifying parameters and measured output power of laser versus delay times show some local maxima and minima at the delay time interval of 6–43？ns.

Stability Analysis of q-axis Rotor Flux Based Model Reference Adaptive System Updating Rotor Time Constant in Induction Motor Drives

q-axis rotor flux can be chosen to form a model reference adaptive system(MRAS)updating rotor time constant online in induction motor drives.This paper presents a stability analysis of such a system with Popov’s hyperstability concept and small-signal linearization technique.At first,the stability of q-axis rotor flux based MRAS is proven with Popov’s Hyperstability theory.Then,to find out the guidelines for optimally designing the coefficients in the PI controller,acting as the adaption mechanism in the MRAS,small-signal model of the estimation system is developed.The obtained linearization model not only allows the stability to be verified further through Routh criterion,but also reveals the distribution of the characteristic roots,which leads to the clue to optimal PI gains.The theoretical analysis and the resultant design guidelines of the adaptation PI gains are verified through simulation and experiments.