I am assuming you are running this with offers/bids defined by what is in gencost. In the first case, the incremental cost of generation between 50 MW and 100 MW of output is $15/MWh. Likewise the incremental benefit for the load between 60 MW and 90 MW is also $15/MWh. For the (lossless) DC OPF problem, this means that the objective function value does not change as the dispatch changes between 60 and 90 MW ... i.e. for the exact bids and offers you are using there is no unique minimizing solution to the DC problem. For the AC problem, the losses create a small price difference between the buses, eliminating solutions with greater than 60 MW of demand, so there is a unique solution.
In the case with the line constraint at 50 MW, once again, you are creating an anomaly by setting the constraint value to fall *exactly* on the corner point of the generator's cost function. If you set it to something slightly less than 50, then the prices will be pretty close to the expected $10 and $18. If you set it slightly greater than 50, then the prices will be $15 and $18. Strictly speaking, the node 1 price for a line capacity of exactly 50 MW is not uniquely defined. It can be anything between $10 and $15. Hope this helps, -- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On May 12, 2011, at 12:58 PM, Santiago Chamba wrote: > Dear Professor Zimmerman, > > I think that there is a probable mistake in the auction method (smartmarket), > specifically in DC OPF. I run a smartmarket and OPF (DC and AC) without fixed > load, i.e., the two nodes system only has generators offers and demand bids > (inelastic). > > When, I run AC OPF the results are correct, but with DC OPF the results may > be wrong, because the inyections and extractions electricity are very > different to the AC responses: > > Node DC OPF DC OPF > Pot Lambda Pot Lambda > MW $/MW MW $/MW > 1 70.8298 15 60.0394 15.00 > 2 -70.8298 15 -60.0067 15.016 > > I think the correct responses for DC OPF is 60 MW in the two nodes. Why are > the AC and DC results so different? > > When, the capacity line decreases to 50 MW, the inyections and extractions > electricity are correct, but the prices changes: > > Node DC OPF DC OPF > Pot Lambda Pot Lambda > MW $/MW MW $/MW > 1 50 11.32 49.99 10 > 2 -50 18.00 -49.97 18 > > I think the correct responses for DC OPF is 10 and 18 ($/MW). Why are the > prices (AC and DC) in the node 1 so different? > > Please, explain me What is my mistake? or Where can I modify the mistake?. > Because I need the model for my investigation. > > Thank > > > > <subasta.m>
