The SESAM calculation is based on an application of the social welfare criterium in combination with market rules. SESAM is maximising the value of the objective function subject to physical constraints; like volume constraints, area balances, transmission and ramping constraints. The objective function to be maximised is the so called social welfare criterium and can be written as:

(1) 

     

Where a represents an area, da is demand in area a and Da  is the demand function in area a, sa  is supply in area a and Sa is the supply function in area a and n is the number of areas.

The model chosen expresses that social surplus, defined in (1) as consumers’ utility minus producers’ cost (represented by function Da and Sa, respectively) shall be maximised subject to minimal requirements:

(2) Volume constraint: For any bid the accepted volume is between lower and upper limits.

(3) Area balances: In any area the physical balance is respected, i.e., for each area accepted supply plus net import equals accepted demand.

(4) Transmission capacities: Any transmission from an area to another area is between lower and upper limits.

(5) Maximal transmission ramp rates: On given lines the transmission between areas a and a’ in hours h and h-1 shouldn’t differ more than a specified maximal allowed deviation. The ramping constraints can be given on one or multiple lines. The set M is defined in terms of geography (i.e. bidding areas), such that each element in M will imply two times 24 constraints. The transmission in the last hour of the previous day is also assumed known on each line.

The model also secures that there exist prices (6) such that

• All single hourly supply bid quantity with bid price below the spot price is accepted
• No single hourlysupply bid quantity with bid price above the spot price is accepted
• All single hourlydemand bid quantity with bid price above the spot price is accepted
• No single hourlydemand bid quantity with bid price below the spot price is accepted

(7) If the spot prices differ between two areas, then the transmission capacity between these areas is fully utilised towards the area with the higher price. If the capacity between two areas is not fully utilized the prices in these two areas shall be equal.

Transferred to the market bids the model reflects the buyers and sellers declared wish to buy/sell at different prices and the therefore calculable theoretical utility/cost resulting from a given market clearing area price.

If all D a are strictly decreasing and all S a are strictly increasing then the solution (if one exists) will be unique. Moreover, the solution found will have associated dual values that may be interpreted as spot prices, and it may be shown that the solution and the spot prices together satisfy the above mentioned minimal requirements (2) – (7).

Observe that the above model is simplified, omitting in particular an hour index h and various types of block bids.