I'm studying a power optimprob which involves a microgrid composed by a PV system, an energy storage, loads and an EV. It is summed up as a big node in which I assume absorbed power is negative (i.e. loads) and generated power is positive (i.e PV), so that I have power balance as:
where Pg is the power flow delivered from (or to) the main grid. The objective is to minimize the integral of Pgrid abs value, so that the power exchanges beetween the main grid and the power grid are minimized, while the control variables are Pbatt and Pev; Ppv and Pload are fixed.
After the setting of constraints , how can I formulate this problem? How can I define my objective function? Have I to set Pgrid too as an optimvar? And how should I treat abs value?