With the increasing share of renewable energy sources in microgrids, systems enhancing the power flexibility at the demand side have become mandatory in microgrid architecture. Thus, the electrical energy storage system has been mostly integrated into microgrids although its capital and operating costs are very high. Hence, diversifying microgrid energy storage based on the end-energy usage can improve the reliability, operating cost, and power demand flexibility of the microgrid. The hereby study integrates an absorption chiller and electrical heat pump coupled to a heat storage into a renewable energy resources-based microgrid and develops its centralized energy management model for both off-grid and on-grid operation modes. The model considers the current energy level of energy storages in the microgrid, current, and forecasted information state to compute the vector-valued decision minimizing a realistic microgrid operating cost. The operating cost includes the energy purchasing/generation, heating/electrical storage, and penalty cost due to load shedding. Hence, such an objective function leads to maximizing the consumption of the generated renewable power, minimizing the energy storage and load shedding cost. The load shedding has been allowed to increase the flexibility in microgrid energy management. However, a high penalty has been imposed on each electrical, heating, or cooling load shedding decision. The decision vector components are thermal and electrical power flow between each energy source to loads and energy storage systems. The problem has been modeled as a Linear Programming with forecasted multi-parametric inputs at different prediction horizons. The effect of the charging/discharging rate and capacity of energy storages, coefficient of performance of absorption chiller and heat pump, prediction horizon, and energy level of storage devices provided to the myopic energy management model has been evaluated for better integration of renewable sources and thermal storage systems into microgrids. Suggestions have been made to improve the microgrid self-consumption, energy efficiency, and myopic decision-making model using the energy level of storage devices obtained from the full look-ahead optimization model. Highlights The optimization problem combining electricity, heating, and cooling is formulated The electrical and thermal storage charging/discharging rate significantly affect the power supplied by the renewable power source decision of the microgrid energy management model. Accurate energy storage level information into the myopic energy management model improves the model decisions. The absorption chiller coefficient of performance greatly impacts the cooling and electrical loads shedding.