On the power exchange, members of the PX put in bids to buy and offers to sell standard products. The bids can vary, in my paper I have focused on complex orders.
Complex orders are introduced by EUPHEMIA, which is the clearing algorithm of the pan-European market coupling. In complex bids, further limits can be imposed on coherent hourly orders/bids. Using the MIC (Minimum Income Constraint) a certain market participant can impose a minimum income limit on the submitted bids. Through the LGC (Load Gradient Constraint), the difference between the allocated amount of energy between two consecutive hours is limited.
The LGC does not take into consideration the fact that the gradient limit of the generation units relates to the supplied power: it presupposes constant power in each hour and limits the changes (jumps) necessary between two consecutive hours. In my thesis, I have developed and introduced the trajectory gradient constraint (TGC): in this case, the power produced by the units ramps linearly within the hour, its average will indicate the volume of the produced energy in the given hour.
In fact, the EUPHEMIA is the formal description of the problem clearing the bids/offers regarding the given constraints, actually large-scale, mixed-integer optimizing problem with quadratic terms (MIQP). I used AMPL software to solve the task. I have completed the available model with the mathematical equations relating to TGC, and implemented it in the solver script.
In the end, I have illustrated the operation of the constraints with an example, plus compare the effects of the different gradient constraints on the variables of the market analysing test cases.