Connection Between Damping Torque Analysis and Energy Flow Analysis in Damping Performance Evaluation for Electromechanical Oscillations in Power Systems

The damping performance evaluation for electromechanical oscillations in power systems is crucial for the stable operation of modern power systems.In this paper,the connection between two commonly-used damping performance evaluation methods,i.e.,the damping torque analysis(DTA)and energy flow analysis(EFA),are systematically examined and revealed for the better understanding of the oscillatory damping mechanism.First,a concept of the aggregated damping torque coefficient is proposed and derived based on DTA of multi-machine power systems,which can characterize the integration effect of the damping contribution from the whole power system.Then,the pre-processing of measurements at the terminal of a local generator is conducted for EFA,and a concept of the frequency-decomposed energy attenuation coefficient is defined to screen the damping contribution with respect to the interested frequency.On this basis,the frequency spectrum analysis of the energy attenuation coefficient is employed to rigorously prove that the results of DTA and EFA are essentially equivalent,which is valid for arbitrary types of synchronous generator models in multi-machine power systems.Additionally,the consistency between the aggregated damping torque coefficient and frequency-decomposed energy attenuation coefficient is further verified by the numerical calculation in case studies.The relationship between the proposed coefficients and the eigenvalue(or damping ratio)is finally revealed,which consolidates the application of the proposed concepts in the damping performance evaluation.

Mode-based Damping Torque Analysis in Power System Low-frequency Oscillations

The mode-based damping torque analysis(M-DTA)method for studying the effect of an external controller on power system low-frequency oscillations is proposed in this paper.First,based on the interconnection model between the system and the controller in the frequency domain,the oscillation loop corresponding to the electromechanical oscillation mode is built,and then the mode-based damping torque of the controller can be calculated.Then,the application of the M-DTA method in the power system is illustrated.The derivation shows that in the single-machine infinite-bus power system,the M-DTA method is completely equivalent to the classical damping torque analysis(C-DTA)method.In the multi-machine power system,the mode-based damping torque directily reflects the effect of the controller on the oscillation mode,overcoming the shortcomings of the C-DTA method in which there is no direct correspondence between the damping torque and the oscillation mode.By deriving the relationship with the residue index,the M-DTA method shows higher accuracy than the residue method in applications,such as controller parameter adjustment.Finally,two example power systems are presented to demonstrate the application of the proposed M-DTA method.Index Terms-Electromechanical oscillation mode,FACTS,interconnection model in the frequency domain,mode-based damping torque analysis(M-DTA),power system low-frequency oscillation,PSS,residue method.

Fast Uncertainty Quantification of Electromechanical Oscillation Frequency on Varying Generator Damping

This letter develops a fast analytical method for uncertainty quantification of electromechanical oscillation frequency due to varying generator dampings. By employing the techniques of matrix determinant reduction, two types of uncertainty analysis are investigated to quantify the impact of the generator damping on electromechanical oscillation frequency, i.e., interval analysis and probabilistic analysis. The proposed analytical frequency estimation formula is verified against conventional methods on two transmission system models. Then, Monte Carlo experiments and interval analysis are respectively conducted to verify the established lower/upper bound formulae and probability distribution formulae. Results demonstrate the accuracy and speed of the proposed method.

Survey on forced oscillations in power system

The oscillations in a power system can be categorized into free oscillations and forced oscillations. Many algorithms have been developed to estimate the modes of free oscillations in a power system. Recently, forced oscillations have caught many researchers’ attentions.Techniques are proposed to detect forced oscillations and locate their sources. In addition, forced oscillations may have a negative impact on the estimation of mode and mode-shape if they are not properly accounted for. To improve the power system reliability and dynamic properties, it is important to first distinguish forced oscillations from free oscillations and then locate the sources of forced oscillations in a timely manner. The negative impact of forced oscillation can be mitigated when they are detected and located. This paper provides an overview of the analysis technique of forced oscillations in power systems. In addition, some future opportunities are discussed in forced oscillation studies.

Online Inertia Estimation Using Electromechanical Oscillation Modal Extracted from Synchronized Ambient Data

An ambient modal framework for inertia estimation using synchrophasor data is proposed in this letter.Specifically,an analytical formulation is developed for the estimation of inertia based on the frequency and damping ratio modes extracted from ambient data.An advantage of the proposed framework is that it can rely on synchronized ambient data under non-disturbed conditions for online estimation and tracking of inertia.Ultimately,numerical simulation studies and physical experiments demonstrate the feasibility of the proposed approach.

Impact of Grid Connection of Large-Scale Wind Farms on Power System Small-Signal Angular Stability

The grid connection of a large-scale wind farm could change the load flow/configuration of a power system and introduce dynamic interactions with the synchronous generators(SGs),thus affecting system small-signal angular stability.This paper proposes an approach for the separate examination of the impact of those affecting factors,i.e.,the change of load flow/configuration and dynamic interactions brought about by the grid connection of the wind farm,on power system smallsignal angular stability.Both cases of grid connection of the wind farm,either displacing synchronous generators or being directly added into the power system,are considered.By using the proposed approach,how much the effect of the change of load flow/configuration brought about by the wind farm can be examined,while the degree of impact of the dynamic interaction of the wind farm with the SGs can be investigated separately.Thus,a clearer picture and better understanding of the power system small-signal angular stability as affected by grid connection of the large-scale wind farm can be achieved.An example of the power system with grid connection of a wind farm is presented to demonstrate the proposed approach.

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.

Small-signal Angular Stability of Power System as Affected by Grid-connected Variable Speed Wind Generators—A Survey of Recent Representative Works

This paper reviews the status and progress of the investigation on power system small-signal angular stability as affected by grid-connected variable speed wind generators(VSWGs).The review is carried out on the basis of a survey of recently published representative papers.Strategies of the investigation made in those selected papers are classified into two groups:1)VSWGs displacing synchronous generators(SGs);2)VSWGs simply being added in a power system.The diversification of the results of the investigation is highlighted in the survey.Careful analysis on two strategies of the investigation is conducted in this paper.It is revealed that in the strategy of VSWGs displacing SGs,there are two factors which could affect power system small-signal angular stability differently:1)Withdrawing the SGs’dynamics;2)adding the VSWGs’dynamics.In the strategy of adding VSWGs in the power system,there are also two affecting factors:1)Change of load flow brought about by the VSWGs;2)dynamic interactions with the SGs introduced by the VSWGs.Hence diversified results of the investigation obtained so far are not only due to the dependence of the investigation on sample power systems used,but also caused by the mixture of different affecting factors.This paper is concluded with a summary of key issues of the investigation for future work.

Small signal stability region of power systems with DFIG in injection space

The modal analysis method is utilized to study the influence of doubly-fed induction generator(DFIG)on electromechanical oscillations.On this basis,the small signal stability region(SSSR)of power systems with DFIG in injection space is evaluated and the corresponding relationship between SSSR boundary and electromechanical oscillations is analyzed.The effects of the locations of DFIG on SSSR are considered.It is found that the boundary of SSSR consists of several smooth surfaces,which can be approximated with hyper-planes in engineering application.With the integration of DFIG,SSSR becomes smaller,thus indicating the deterioration of the small signal stability of the system.The 11-bus system with four generators is used to illustrate the proposed method.