Application of Gramians method for smart grid investigations on the example of the Russky Island power network

Grobovoy, A.; Shipilov, V.; Arestova, Anna; Yadykin, Igor B.; Afanasyev, Valery; Iskakov, Alexey B.; Kataev, Dmitry E.

doi:10.1109/irep.2013.6629352

Cited by 10 publications

(3 citation statements)

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“…First applications of Gramian technique for investigation of EPS static stability relate to stability analysis of Kundur test model of two district power system (Ahmetzyanov et al, 2012) and the model of Russky Island power system (macrogrid) (Grobovoi et al, 2013). This investigation confirmed mentioned earlier properties of gramians and subgramians, and detected a number of peculiarities of gramian technique numerical realization, in particular numerical instability of large dimension Faddeev matrices calculation.…”

Section: The Evaluation Of Eps Stability Loss Risk By Gramian н2-normsupporting

confidence: 65%

“…The method operates by decomposing the Gramian matrix that is a solution of the Lyapunov or Silvester equation into a spectrum of matrices that make up these equations. It is more effective comparing to modal analysis as it allows to prescribe the criterion of EPS stability loss risk (Sukhanov, 2012), and also to evaluate the interaction of illstable system modes (Grobovoi, et al, 2013). To develop immune system it is necessary to create virtual analyzer (soft sensor) of the stability loss threat.…”

Section: Introductionmentioning

confidence: 99%

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Stability in small signals investigation of nonlinear dynamic power systems

Vassilyev

Yadikin

Bakhtadze

et al. 2014

IFAC Proceedings Volumes

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Section: The Evaluation Of Eps Stability Loss Risk By Gramian н2-normsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Stability in small signals investigation of nonlinear dynamic power systems

Vassilyev

Yadikin

Bakhtadze

et al. 2014

IFAC Proceedings Volumes

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“…In order to illustrate how the proposed method can be applied to the stability analysis of power grids, a Simulink model of the real Russky Island power network (Grobovoy et al (2013)) has been employed. In the preliminary analysis of the dynamic properties of this network, a test model shown in Figure 1 has been used.…”

Section: Power System Model Descriptionmentioning

confidence: 99%

Stability analysis of electric power systems using finite Gramians**This work was supported by research project No.14-08-01098-a of the Russian Foundation for Basic Research (RFBR).

et al. 2015

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We present an extension of the method of eigenmode decomposition of Gramians proposed earlier for the the small-signal stability analysis of dynamical systems. In this paper we derive the spectral decomposition for finite Gramians on any time interval and with arbitrary initial conditions. These expansions allow both a stability analysis of non-stationary systems and a monitoring of instability development in unstable systems. Eigen components in the expansion of Gramians on a finite interval of time we called finite sub-Gramians. Because each sub-Gramian is associated with a particular eigenvector, the sources of instability can be easily localized and tracked in real time. We perform a simulation experiment in which finite subGramians are used to analyze the development of instability arising in an actual power grid on Russky Island when it is disconnected from the mainland network.

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