Fast Calculation of Saddle-Node Bifurcation Point in Islanded Microgrid Based on Levenberg-Marquardt Algorithm

Liu, Kaicheng; Lin, Liheng; Tang, Kunjie; Dong, Shufeng

doi:10.1109/cieec50170.2021.9510839

Cited by 1 publication

(2 citation statements)

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“…The application of the bifurcation theory has been performed for studies such as, voltage collapse [14], flexible AC transmission system devices [15], sub-synchronous resonances [16], among others [17]. Furthermore, the analysis of microgrids with different controls using the bifurcation theory has been presented in recent works [18][19][20][21][22][23][24][25][26]. The stability analysis of a synchronverter-dominated microgrid based on bifurcation theory was presented in [18]; in this work, the system is modeled in DQ frame and an eigenvalue analysis is performed considering three different bifurcation paramenters, additionally, the results show that the modification of the reactive power coefficient provokes a Hopf bifurcation in the system.…”

Section: Introductionmentioning

confidence: 99%

“…A generalized model is proposed in [24], this model is given by a block diagram approach used for modeling the microgrid, then the system initialization is obtained via a load flow method and the eigenvalues are computed, bifurcation analyses and phase diagrams are presented showing the Hopf bifurcations under different cases. Two saddle-node bifurcation point algorithms for islanded microgrids are presented in [25], these approaches use the power flow method as base to obtain the feasible and non-feasible operational regions after an increase of load in the system, then, the proposed algorithms are used to search between these regions the saddle-node bifurcation; to verify the algorithms, four case studies are implemented and comparisons among traditional methods presented. Recently in [26], the bifurcation analysis was used to predict the parameter stability margins with and without secondary control in islanded droop-controlled microgrids; in this work, the system is modeled in the DQ reference frame and an eigenvalue analysis is performed considering different parameters.…”

Section: Introductionmentioning

confidence: 99%

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Stability Boundary Analysis of Islanded Droop-Based Microgrids Using an Autonomous Shooting Method

2022

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This paper presents a stability analysis for droop-based islanded AC microgrids via an autonomous shooting method based on bifurcation theory. Shooting methods have been used for the periodic steady-state analysis of electrical systems with harmonic or unbalanced components with a fixed fundamental frequency; however, these methods cannot be directly used for the analysis of microgrids because, due to the their nature, the microgrids frequency has small variations depending on their operative point. In this way, a new system transformation is introduced in this work to change the droop-controlled microgrid mathematical model from an non-autonomous system into an autonomous system. By removing the explicit time dependency, the steady-state solution can be obtained with a shooting methods and the stability of the system calculated. Three case studies are presented, where unbalances and nonlinearities are included, for stability analysis based on bifurcation analysis; the bifurcations indicate qualitative changes in the dynamics of the system, thus delimiting the operating zones of nonlinear systems, which is important for practical designs. The model transformation is validated through time-domain simulation comparisons, and it is demonstrated through the bifurcation analysis that the instability of the microgrid is caused by supercritical Neimark–Sacker bifurcations, and the dynamical system phase portraits are presented.

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