Microgrids (MGs) are playing a fundamental role in the transition of energy systems towards a low carbon future due to the advantages of a highly efficient network architecture for flexible integration of various DC/AC loads

distributed renewable energy sources

and energy storage systems

as well as a more resilient and economical on/off-grid control

operation

and energy management. However

MGs

as newcomers to the utility grid

are also facing challenges due to economic deregulation of energy systems

restructuring of generation

and market-based operation. This paper comprehensively summarizes the published research works in the areas of MGs and related energy management modelling and solution techniques. First

MGs and energy storage systems are classified into multiple branches and typical combinations as the backbone of MG energy management. Second

energy management models under exogenous and endogenous uncertainties are summarized and extended to transactive energy management. Mathematical programming

adaptive dynamic programming

and deep reinforcement learning-based solution methods are investigated accordingly

together with their implementation schemes. Finally

problems for future energy management systems with dynamics-captured critical component models

stability constraints

resilience awareness

market operation

and emerging computational techniques are discussed.