Determination of worst case loading margin of droop-controlled islanded microgrids

The determination of an islanded microgrid proximity to voltage instability is essential for its operation with an adequate security margin. This paper presents an algorithm for determining the worst case loading margin of droop-controlled islanded microgrids. The problem is formulated as an optimization problem to determine the shortest distance to voltage instability (i.e. the closest saddle node bifurcation point). A detailed microgrid model is adopted to reflect the special features of droop controlled islanded microgrid systems where; 1) the system frequency is a power flow variable, and 2) the power produced by the different DG units is dependent on the system power flow variables and cannot be pre-specified. The optimization problem is subject to different system operational constraints including; the power flow constraints, voltage and frequency regulation constraints and unit capacity constraints. Different numerical case studies have been carried out to test the effectiveness and the robustness of the proposed algorithm.