The small signal stability of a MG is extensively assessedusing eigenvalue analysis. State space matrix is obtained fromthe complete state space model of MG. Eigenvalues are theroots of the characteristic equation of linearized state matrix.With help of these eigenvalues the system’s damping anddifferent frequency components can also evaluated.

Also effectof changes in state variables in a particular mode on systemcan be analyzed with eigenvalue sensitivity analysis. Theequation for sensitivity analysis is given as:where iis the itheigenvalue, is any system parameter, vis the left eigenvector and uis left eigenvector. Sensitivityanalysis to some extent can help in optimizing the controllerparameters while designing.iiThe test system as shown in Fig.

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4 consists of two inverterinterfaced DG’s of equal rating (10 KVA),with AC side voltagerating 230 V, frequency 50Hz. Values of other parametersare mentioned in Table I. For dynamic stability analysis,eigenvalues for the state matrix are obtained. In this analysissteady state operating points of state matrix are obtainedfrom simulation using MATLAB/SIMULINK. Eigenvalues btained for complete microgrid model is shown in Fig.

5.Eigenvalues being negative states that the system is stable.More negative the eigenvalues more stable will be the system.Whenever there is any disturbance, in traditional power systemthe inertia constant takes care of the situation. But whenthe inertia reduces or becomes zero, in MG other systemparameters such as the droop coef?cients, line impedance,reactance etc.

gets affected. If we increase the value of droopcoef?cient we can see from Fig.7. that the eigenvalues startmoving more towards zero axis. They are becoming lessnegative, hence the system can become unstable if the increasein value continues.

Such a plot can help us to take preventivemeasures before the system may become unstable. At the sametime if the value of line reactance is increased it can be seenfrom Fig.8. that the eigenvalues become more negative andthus help to improve system stability. And if it decreases it alsocan make system unstable. Thus by analysing the variation ineigenvalue plot at various instants we can keep an eye on thesystem’s stability condition and accordingly can take measuresto prevent the instability conditions if any.

Inertia is one of the crucial parameters for stable operationof power system. Increased penetration of RES basedgeneration reduces inertia and affects the frequency dynamicsof the system and its stability. So with more and more DGpenetration to main grid, it is necessary to ?nd ways thatcould handle the inertia property of the system. A small signaltate space model of a microgrid was presented in the paperthat included inverter, network, and load. The eigenvalues ofsystem matrices were calculated and variation in eigenvalueswith variation in droop coef?cients and line reactance wereobtained and plotted.

The results showed that the stability ofpower system will be risked if droop coef?cients increases.Increase in droop coef?cients indicate a decreased inertia.Hence it is seen how reduced inertia can make system unstable.Similarly decreasing line reactance can also make systemunstable.


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