How can I minimize absolue value in a power optimprob?

Hi everybody,

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:

Ppv+Pbatt+Pev+Pload=Pgrid

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?

[Rik]

I don't understand your system well enough to understand what your question is. It sounds like you first need to find out what exactly you want to know before you can start with the implementation.

Assuming from the start that you'll need optimvar sounds like an XY problem.

Have a read here and here. It will greatly improve your chances of getting an answer.

[Danny]

Hi @Rik,

thanks for your suggestions. My problem sounds like a variant of this Matlab example: https://it.mathworks.com/matlabcentral/fileexchange/73139-microgrid-energy-management-system-ems-using-optimization?s_tid=srchtitle&#examples_tab. In my specific case, I would like to find Pbatt and Pev profiles (subject to power and energy constraints) in order to minimize abs value of Pgrid.

Answer 1

[Matt J]

The objective is to minimize the integral of Pgrid abs value... while the control variables are Pbatt and Pev; Ppv and Pload

If your unknown vector is x=[Pbatt;Pev; Ppv; Pload] then your problem sounds like the L1-norm minimization,

where C is just C=[1;1;1;1] and C*x=Pgrid.

If I've interpreted correctly, then minL1lin is applicable

https://www.mathworks.com/matlabcentral/fileexchange/52795-constrained-minimum-l1-norm-solutions-of-linear-equations

[Danny]

Hi @Matt J,

thanks for your support. Ppv and Pload are known vectors that I load from a .mat file, that stand for photovoltaic production and domestic load consumption. Then, with your formulation, they will be constant term "b", if we think a linear system in the form Cx=b and if I interpreted correctly.

[Matt J]

Yes, that sounds right.