This paper presents a comprehensive model of dynamic optimal operation management of the smart nano-grids (NGs) including the micro wind turbines (WTs) and micro photovoltaics (PVs) as renewable energy sources (RESs) while micro turbines (MTs) and fuel cell (FC) are considered as non-RESs. Furthermore, two types of lead-acid and lithium-ion batteries are considered besides the three types of controllable, curtailment-able and must run loads to increase the flexibility of the proposed formulation. The different objective functions of NG operation problem to be minimised include operating cost, environmental damage cost of pollution gases and exchanged power cost with the main grid. Also the power losses of batteries are modelled using the quadratic functions based on types and output powers of considered batteries, while these losses impose additional cost to operation cost functions of batteries. A modified teaching-learning-based optimisation (MTLBO) algorithm is used to cope with the multiobjective problem considering the constraints.