Small Signal Stability Analysis Of Microgrid Based On Matrix Perturbation Theory

Microgrid has attracted increasing attention as an effective means of integratingdistributed generation units into the power systems. The increasing penetration ofdistributed generation units has put forward higher demand for the microgrid stableoperation. This thesis mainly focuses on the small signal stability analysis of amicrogrid. The major work can be summarized as follows:(1) Small signal models of distributed generation units are analyzed based on twodifferent grid-connection types, namely inverter-interfaced distributed generationunits and generator-interfaced distributed generation units. Besides, a comparativeanalysis is made on the small signal models of three typical controls ininverter-interfaced distributed generation units. Taking into account the characteristicsof sparsity and partition of the small signal models, a sparse filling and addressingapproach for constructing state matrix based on improved cross chain table method isadopted in the small signal stability calculation. On these basises, the extensive andregional distribution characteristics of eigenvalues in a microgrid are then illustratedin detail, revealing the corresponding influence factors as well.(2) A matrix perturbation based approach is proposed for the sensitivity solutionand analysis of eigen-solutions in a microgrid. Matrix perturbation theory isintroduced systematically, based on which parameter perturbations are utilized toanalyze the construction characteristics of the state matrix. The sensitivities ofeigenvalues and eigenvectors to control variables are then obtained and analyzedaccording to different spatial distribution characteristics of eigenvalues, namelydistinct eigenvalues and multiple eigenvalues. Through the proposed approach, thesensitivities of eigen-solutions can be calculated with satisfactory accuracy. Not onlyare the complex derivations of sensitivity formulas concerned in analytical methodavoided, but also repeated solutions of eigenvalue problem involved in numericaldisturbance method is no longer required.(3) In order to improve the small signal stability of a microgrid, a novel approachbased on matrix perturbation theory is proposed for the coordinated optimization ofthe droop coefficients in inverter controllers of a microgrid. Rigorous parameterperturbation analysis is applied to the droop coefficients of inverter controllers toidentify the manner and degree of their influence on the system state matrix. Furthermore, the influence factors are investigated as well. An eigenvalue-basedobjective function is proposed, aimed at ensuring the stability of the system,enhancing the damping characteristics, and maintaining the stability margin for a widerange of operating conditions. In the parameter-optimization process, matrixperturbation theory combining with sequential quadratic programming is applied insolving the minimization problem with constraints. In the examples, theparameter-optimization process, the time-domain simulations, and the robustnessanalysis of the optimized coefficients are carried out and analyzed in detail.Theoretical analysis and evaluation results have confirmed the effectiveness of theoptimization approach, the feasibility of the objective function, and the robustness ofthe optimized parameters.