I'll start with your last question. The extensible OPF architecture in MATPOWER supports only linear user constraints. The user cost terms can have a quadratic form with additional features detailed in section 5.3.1 of the manual.
So, I don't see a way to add the costs you want directly to the current model. However, I do have an idea. How about this? To simplify the explanation, let's suppose each area interchange can be defined as a summation of Pf (power injected into the "from" end) of a subset of branches (the tie lines). Then for each tie line do the following: 1. If bus f is the current "from" bus for the branch, add a new bus f' and connect the tie line to bus f' instead of bus f. 2. Add a new dummy generator at bus f and another at bus f', to represent the flow in the branch. 3. Add an equality constraint between the voltage angle at bus f and at bus f'. 4. Add an equality constraint between the voltage magnitude at bus f and at bus f'. 5. Add an equality constraint between the power injected by the new generator at bus f and the negative of the power injected by the new generator at bus f' (one constraint for real power and one for reactive power). The standard OPF solution for this new network model should match that of the original, but now you have optimization variables that are equal to the flows in the tie lines and you can put costs on them. You can use N and rhat in the user-defined cost model to compute the deviation from the scheduled interchange and put a cost on that. Would that give you what you are looking for? -- Ray Zimmerman Senior Research Associate 211 Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Dec 12, 2010, at 2:20 PM, Álvaro Jaramillo Duque wrote: Hi all I am interested to add an objective function to the OPF formulation. The objective of the function is to minimize the deviation of the power exchange (active and reactive) between areas in a big power system, calculation the deviation from the start point. The main idea is maintain the power exchange between areas as closer is possible to the start point. When other variables had changed, load and generation. I am not sure if I can do this using the callbacks functions? Another question, it is possible to set a non-lineal user function and constrains using the callbacks functions? Thanks, Best Regards, Álvaro Jaramillo Duque
