This work proposes a systematic approach for the adaptive identification and implementation of efficient power management strategies (PMS) in the course of operation of hybrid renewable energy microgrids. The approach is based on the temporal evolution of the system power grand composite curve (PGCC), which is adaptively shaped on-line and within short-term time intervals to form a sequence of decisions indicating the instant and duration of activation of different subsystems. It builds on from previous work where the potential for system performance enhancement could not be exploited through pre-specified PMS identified off-line. More specifically, it involves a stored energy targeting step that exploits the PGCC to identify the desired operational profile of an accumulator during a prediction horizon in order to satisfy the system operating goals. The identified energy targets are subsequently enforced through a sequence of control actions that enable the exact matching of the PGCC hence resulting in a new PMS. The method is elaborated graphically for multiple potential operating goals and is supported by a formal mathematical model that captures system structural and temporal characteristics. It is implemented on an actual hybrid microgrid considering multiple RES-based energy generation and storage options for expected and unexpected weather conditions.