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For low-voltage autonomous microgrids, the essential goal is maintaining stable voltage and frequency throughout its network for the smooth operation of distributed loads. The other goal is to maintain proportionate power-sharing between multiple sources connected through voltage source converters (VSCs). For the particular case of a heavily loaded microgrid, any further increase in demand poses new problems. The VSCs proximate to the loads may overshoot beyond its maximum ratings. Owing to which the stability of the power supply, as well as the longevity of VSCs, may get compromised. Also, these sources provide power under varying composite loading conditions comprising both linear and non-linear loads resulting in unbalancing in its network. To overcome these problems, a decentralised fast terminal sliding mode control strategy for active power-sharing between parallel VSCs has been proposed. A detailed mathematical model based on Lyapunov's stability theorybased study is designed to establish the operating stability of the proposed controller. To validate the proposed control strategy, MATLAB-based simulation results are provided for possible loading scenarios. A comparative study for performance evaluation between the proposed controller and a conventional proportional-integral-based controller is further carried out. Finally, the performance of the proposed controller is also validated in real-time scenario.

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One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.