To engage an optimization problem, you should try to specify the respective variables you try to optimize, first. In your case: which dependend variable do you want to optimize, and with which variables would you want to achieve it in an optimal way.
what do you mean by dividing the power system into several MGs?!!
in power systems, we know the location of the MGs, because we build the MG in the specific locations with their own specific characteristics. we are not dividing or decomposing the system into several MG!!! You need to build an MG.
IMO the statement "we can divide the large power system into a number of μGs" requires some more clarification.
There are some (people/works) that advocate the use of μGs as the main module for future smart grid(s).
This does not mean that any "large" power system can be arbitrarily divided into a number of μGs; different migration strategies, constraints etc can be identified.
Thus, as stated, the decomposition of an existing(?) power network into several μGs is an ill defined problem.