The AC OPF and DC OPF are different problem formulations. AC includes the modeling of voltage magnitudes and reactive power and has non-linear constraints. DC, on the other hand, make approximations to eliminate voltage magnitude and reactive power and includes only linear constraints. They are different optimization problems and one should expect different solutions, both primal and dual (dispatches and prices). In both cases, the bus lambdas from the OPF are the dual variables associated with the power balance equations (equation (5.2) in the manual). How they are computed depends on the solver. If you are using the standard MIPS solver and want all the gory details of how it works, have a look at section A.4.
Have you read the MATPOWER Technical Note 1 on Uniform Price Auctions and Optimal Power Flow? The relationship between the lambda and the market clearing price is explained in great detail there. If you are using the default market type (5), the market clearing price for a generator is equal to the lambda at the bus, unless the lambda is less than the offer, in which case the clearing price is set to the offer price (see Section 5.2 in the Tech Note). At this point, I'm happy to attempt to answer any specific questions you have about MATPOWER that are not covered in the User's Manual or the Tech Note. However, this is starting to feel like a personal tutorial, which I'm afraid I can't afford to offer. -- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Mar 3, 2011, at 10:01 AM, Geev Mokryani wrote: > > It is better to ask this question like this > > 1. what is the relationship between Lambda and market clearing price? > > 2. why generators must pay in the case of Dc the value of Lambda? > > Best Regards > > Geev > > > <case6ww inputs.m> On Mar 3, 2011, at 6:02 AM, Geev Mokryani wrote: > Dear Prof. Zimmerman > > Maybe I couldn't express my mean well. My questions are as follow: > > 1.For example, in case6ww, in the case of AC load flow how much money are > received by loads and generators? while in the case of DC load flow theses > values are same. for example for generator 2 the value of Lambda and quantity > sold are different while in DC are equal. > 2.the price of quantity sold and the Lambda are different?why? > 3. How these cost (Lambda) have been computed? I want to know in MATPOWER by > what formulas and methods you have computed Lambda? > I will be appreciate if you address the formulas. > > the input data for case6ww are attached. > > Best Regards > > Geev > > > <case6ww inputs.m>
