Fischer-Burmeister-Based Method for Calculating Equilibrium Points of Droop-Regulated Microgrids

This paper gives theoretical foundation to a procedure for modeling in a simply way the behavior of a droop-regulated islanded microgrid when, due to reserve scheduling considerations, the power reserves might be exhausted. The main problem observed for computing the operating point of those microgrids is that the droop formulation that is to be entered in the computation depends on the knowledge of the final result, which indeed means that the solution by means of Newton-Raphson-like methods is hindered. The proposed procedure reduces the complexity by formulating the problem as a complementarity problem. A discussion is offered then on the specific problem of droop formulation: two states are possible (with and without power limit reached), with the particularity that the power must be considered constant only when the power limit is reached, whereas the frequency can freely vary in both states, searching for an equilibrium in the load share among all the generation units endowed with droop regulation. Further, the problem is simplified by resorting to the use of Fischer-Burmeister NCP-functions (NCP for nonlinear complementarity problem), which substitutes the piecewise-defined droop function by an only scalar function (Fischer-Burmeister function) that makes the problem tractable to be solved by Newton-Raphson-like methods. The paper concludes with an exposition of numerical simulations in which the consequences of considering the power exhaustion on stability and operating points are demonstrated.