Investigation into the stability of low-inertia micro-grids

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This work examines the stability of low inertia micro-grids (MGs). The lack of inertia in such power electronics dominated grid is a pressing matter that directly impacts its operation and stability. The investigated MG is formed by power electronics-based DC-AC converters; each of them is controlled by a virtual inertia controller to emulate certain characteristics of the existing synchronous generators-based grid. Two methods to study the stability of the given MG are discussed. The first one is a systematic construction of Lyapunov’s energy function using Popov’s criterion. This function is used to construct a region of attraction (ROA) that defines the stability boundary of the multi-VSG MG. A systematic calculation of the Critical Clearing Time is also introduced here to provide a quantitative measure of MG stability to complete the study. The second method to study the MG stability is a proposed convex hull-based trajectory reversing method. The proposed method estimates and enlarges the ROA of grid connected VSGs MG, regardless of complexity of its model or control scheme. A family of trajectories initiated close to the VSG equilibrium point is generated and evaluated at successive time steps Δ𝑡. Then, convex hull algorithm finds the minimum region that contains all these points. Moreover, this work proposed a new technique to define the set of initial points needed by the algorithm. Compared to Lyapunov’s method, the proposed method does not rely on finding a specific Lyapunov function or satisfying certain conditions. A case study is conducted to validate the algorithm performance and its estimated ROA by both methods. Finally, this work also proposes a new nonlinear controller that enhances system response and increases stability. The proposed enhanced virtual inertia controller (EVIC) changes VSG inertia as a function of the disturbance introduced to the system. It relies on a simple tunable nonlinear equation without any extra sensors, complex algorithms, or prior knowledge of MG configuration or parameters. The results show the validity of the proposed EVIC to reduce oscillations in grid frequency and output power, as well as increase the area of attraction, and hence, MG overall stability and robustness.
Micro-grid, Low inertia, Nonlinear analysis