I can't really help you with the transformer modeling, but the binding upper voltage constraint at the substation is expected. In an OPF, losses, and therefore system costs, can be reduced by increasing the voltage everywhere. So usually the OPF will increase the voltages until at least one upper limit is binding somewhere. In a radial distribution network, this is typically at the substation.
If it is not converging, the question is whether lowest voltage in the system can be kept feasible even with the substation at the upper voltage limit. As the load increases, it will tend to pull down the voltages at the ends of the branches of the radial tree, unless there is some additional VAr support there. You could try relaxing the lower voltage bounds to see if you get a convergent solution. If you do get a solution, and some of the voltages are below the original lower limit, then you've found the reason for the original non-convergence. -- Ray Zimmerman Senior Research Associate 419A Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645 On Mar 8, 2012, at 11:44 PM, M Nightingale wrote: > I am trying to model a radial network that represents the pos-sequence on a > distribution model. The substation is 138 baseKV, and the remaining network > is on 4.16 baseKV. I placed a generator at the substation. > > When I have very little demand (say less than a few MWs), the OPF converges. > As I increase demand, the |V| value at the substation is high and binding at > the upper bound (0.9 <= |V| <= 1.10) and the OPF does not converge. > > I have not yet modeled the transformer connecting the from the substation to > the distribution network. I've tried to set the tap ratio to various values, > but no matter what I try, always is the case that |V|=1.10 p.u. binding at > the substation. > > How do I model the transformer to make the solution converge? Or, does anyone > have any idea what might be happening here? What am I maybe doing wrong? > > Here are the r,x, and b values for the branch from the substation (138 kV) to > the distribution network (4.16 kV). I set the baseMVA to 100. > > > r_pos-seq = .0904 Ohms > x_pos-seq = .2795 Ohms > r = r_pos-seq * (baseMVA / baseKV ^ 2) = 0.5224 p.u. > x = x_pos-seq * (baseMVA / baseKV ^ 2) = 1.6151 p.u. > b is negligible. > > Thanks, Miranda
