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In the following table a primer of the most important class of problems is presented. As noted before we distinguish the monopolist systems from those market based.

#### Market based Systems

##### TSO: Balancing Markets clearing

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:

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 Optimal Power Flow

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1. Pure Price Taker
2. Supply function equilibrium
3. Residual Supply
4. Cournot competition
5. Bertrand competition
6. Other more complicated models could include multi market maximum profit optimization models. In these models one tries to optimally allocate energy of power units among the different markets on cascade possibly with different clearing logic while respecting the operating - often multi periodal - restrictions of the power units. Also, if zonal prices are considered by the electricity market, some form of arbitrage could be tried by GenCos with production plants geographically spread across the system.

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 OPF

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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:

• Thermal units: Thermal (including nuclear) power plant are modeled in a somehow detailed manner. Main constraints and objective function include:

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).
• Hydro Units: Also hydro units are modeled in a somehow detailed manner. Main constraints include:

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.
• Renewable non programmable (i.e. wind and solar): These power plants do not actually have operational constraints but due to their intermittency the TSO (or the monopolist) must carefully forecast their production profile perhaps by geographical aggregation. In turns the inherent uncertainty in their (forecasted) schedule calls for stochastic-like approaches.

Contributor:

Dr. Fabrizio Lacalandra, QuanTek