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This study presents a comprehensive formulation to represent islanded microgrids, where the base power is obtained from wind energy (doubly fed induction generators), and the ancillary services and energy buffering are obtained from distributed resources, either distributed generation or energy storage. Furthermore, this study presents an approach to solve the operational constraints (pitch regulation, power limits, etc.) by transforming the problem into a variational inequality problem. This eventually leads to a constrained version of the original unconstrained problem that preserves its solvability as if it was an unconstrained problem; of special interest because, as shown in the study, the errors of not considering the operational constraints may be large. The formulation presented is of interest for finding the operating point of such a microgrid, and to directly represent the equality constraints that limit the feasibility set of the optimisation problems.