Formulation of recourse function and l-shaped method


Hi everybody, I came here after I couldn’t figure it out myself dispite using all books and youtube material available. I formulated a minimization problem and want to bring it into an L-shaped method for solving it in matlab. This is basically the problem: cost © minimal use of wind (w) and photovoltaic § power in 4 different areas (M) to satisfy electricity demand (D) in combination with 3 different electricity storage types (j), x states the amount of peak power, k the capacity of storage installed.

Min_{x_w^M,x_p^M, k_j} \sum_{M} x_w^M * c_w + x_p^M * c_p + \sum_j k_j*c_j

The stochastic input is given through the weather which influences the operating grade of wind (f^M_wst) and photovoltaic (f^M_pst). f^M_wst and f^M_pst are vectors containing all scenarios. scenarios Of course, demand (D) has to be satisfied each hour of the year (t=1,…,8760) through production of w and p, and saved energy in storages. \alpha^j states the maximum outflow of energy from storage j :

\sum_M x^M_w *f_{wst}^M + \sum_M x^M_{pst} * f_{pst}^M \sum_j \alpha^j e^{j+}*k^j \geq D_t

It is supposed to be a two-stage linear optimization model, formulated in an L-shaped Method. Any tips and recommendations are welcome!!!

(Michael C. Grant) #2

This is not the proper forum for general modeling assistance. For that you need something like Math.SE, OR-Exchange, etc. Once you have a CVX model running, feel free to come back for support.

(Michael C. Grant) #3