At the heart of short term optimization problems there is the (short-term) Unit Commitment (UC). This problem requires to optimally operate a set of hydro and thermal generating units, over a given time horizon in order to satisfy a forecast energy demand at minimum total cost. The generating units are subject to various technical restrictions, depending on their type and characteristics. The UC is typically a large-scale, non-convex complex optimization problem.

Here we list several optimization problems from different entities perspective:

In both monopolist and market based models of course production power plants dynamics have to be modeled in a correct way. In the short term, GenCos must consider these constraints in the most detailed way, here we sketch some of the most important:

    1. quadratic cost curves possibly including some important (interdicted) valve point.
    2. min and maximum stable production.
    3. ramp rates and start up rates, possibly depending on the working points for bigger coal plants.
    4. complex operating dynamics for Combined Cycle Gas Turbine (CCGT) that have several Gas Turbine (GT) coupled with Steam Turbine (ST).
    1. Water-to-Power non linear relationships, for thin basin the bilinear dependency of the basin level, together with the discharge, can be included. This severely complicates the models.
    2. Complex cascade dynamics, including delays in the water flows from one basin to another. These delays can be also of different hours for big cascade and as a results their consideration strongly couples the decision variables along the time dimension.
    3. Additionally a forecast of possible natural inflows must be considered, due to rain or snow melt in some situations.

CPLEX applications


Prof. Antonio Frangioni, University of Pisa

Dr. Fabrizio Lacalandra, QuanTek