See responses below ... On Mar 1, 2012, at 7:25 AM, Hua Bowen wrote:
> Dear All, > > I am dealing with reliability assessment of a real-life system. This > system has 5370 nodes. I converted all the loads into dispatchable > loads and the power flow converged. > > I planned to use dispatchable load model to determine the amount of > load shedding in different contingencies. So I set the cost for all > real generators to zero and the cost for all dummy generators (used to > model dispatchable loads) to 1$/MW. However, when I was running AC OPF > on this system, using default solver, MATPOWER says that “Matrix is > singular” and “Numerically failed”. I tweaked the all the voltage > limits to 0.7 p.u. – 1.3 p.u., “Matrix is singular” message > disappeared, but OPF still didn’t converge. If no load shedding is required and all generator costs are zero, then the optimization surface is very flat ... i.e. the objective function will be constant no matter what the generator cost. I normally use the actual generator costs for the real generators and some very high value, representing the value of lost load, for the dispatchable loads. > Also, I tried MINOPF, TRALM, and even DC OPF, it still won’t converge. > > I tried to use the result of AC power flow as the initial value for AC > OPF, MATPOWER says that "makeAvl: For a dispatchable load, PG and QG > must be consistent with the power factor defined by PMIN and the Q > limits." I wonder why? Hmmm ... well, the dispatchable load model was designed with only the OPF problem in mind, so it's probably not behaving as expected in the power flow problem. For the power flow, were you setting all of the loads at their nominal values (i.e. PG = PMIN)? My guess is that for (at least some of) the buses with only dispatchable loads, the bus type was set to PV, which means that the power flow will change the QG in order to maintain the voltage setpoint, thus violating the constant power factor constraint. Setting the bus type to PQ for these buses should fix that. Unfortunately, for buses with both generators and dispatchable loads, the power flow computes the correct net QG, but then distributes it evenly across the "generators" (including dispatchable loads) at that bus. So it would also mess up the dispatchable load power factors. I suppose this could be corrected for manually after the fact, but that's not currently in the code (something for my to-do list). Also, many of the solvers select their own starting point anyway. MINOPF is one of the few that attempts to use the starting point you provide. Unfortunately, 5370 buses is pretty big for MINOPF. > I checked the branch flow limits. They are quite reasonable. I set > voltage limits to all zero. It didn’t help. I would use non-zero gen costs, keep the voltage limits at something reasonable (0.9-1.1) and try setting the line limits to zero (to disable them) to see if that allows it to converge. > I wonder what is wrong. Is my approach to this problem appropriate? > Anything wrong with my setting of gencost? I think your approach is fine, except for the zero costs in gencost and the extreme relaxing of the voltage constraints. I think that trying to start with a power flow solution (that respects the constant power factor constraints of the dispatchable loads) is a good idea. Then have a look at the voltages, branch flows, reactive dispatches to see which ones (if any) are violating the OPF constraints. > By the way, I wonder whether MATPOWER allows multiple slack buses in > AC OPF? In my case I tried both multiple and single slack bus. Won’t > help. MATPOWER does allow multiple reference buses in the AC OPF. Keep in mind that for the OPF problem there is no concept of "slack", as in generation balance, only the concept of voltage angle reference. So, I would never use multiple reference buses unless the system is islanded, in which case you want a single reference bus in each island. Hope this helps, -- Ray Zimmerman Senior Research Associate 419A Warren Hall, Cornell University, Ithaca, NY 14853 phone: (607) 255-9645
