I like to solve the original case first because, in many cases, the values of QG are either inexact, zero, or completely wrong; this is because (for PV buses) QG is actually an output of the powerflow calculation, not an input.
By the way, I didn't check how MATPOWER behaves when switching the bus type to 1 (PQ) while leaving the generator connected. Maybe it does exactly the same kind of thing that I did explicitly, i.e. treating PG,QG as a load (just by inverting their sign). If so, my script could be simplified. -- Jose L. Marin Grupo AIA Edificio ESADECREAPOLIS Av. de la Torre Blanca, 57 08172 Sant Cugat del Valles, SPAIN Tel: +34 935 044 900 Cell: +34 627 481 474 Fax: +34 935 802 188 http://www.aia.es 2016-07-28 15:21 GMT+02:00 davor sutic <[email protected]>: > Thanks for the input and especially for the provided script, Jose. > Although I'm still analyzing, I just wanted to ask for a quick > clarification. You state "take a particular PV bus and convert its > generator injections PG,QG (values taken from the solved case!) into a > fixed PQ load", wouldn't that be the Pg and Qg values already defined for > the generator at that bus (i.e. the ones already specified in the generator > data section of that case)? In that case, there would be no need to solve > first for the base case and then to convert PV buses to PQ equivalents. > > On Thu, Jul 28, 2016 at 2:14 PM, Jose Luis Marín <[email protected]> wrote: > >> Hello Davor, >> >> This is actually a very interestng question from the point of view of the >> numerical stability of the equations. I asume that by "changing the bus >> type PQ --> PV" you mean the following: start by solving a given case, then >> take a particular PV bus and convert its generator injections PG,QG (values >> taken from the solved case!) into a fixed PQ load, then remove the >> generator, and finally switch the bus type to PQ. Then you repeat this >> progressively until you're left with no PV buses. >> >> The resulting system obviously shares the same mathematical solution, >> but, as you're guessing, trying to solve the converted system definitely >> shows some numerical effects. The way I understand it, there are >> differences coming from these two sources: >> >> - The condition number of the Jacobian degrades: the Jacobian matrix >> of the NR method (and also FD methods) is related to the admittance matrix >> of the network, which is in turn related to the Laplacian matrix of the >> graph representing the transmission grid. Swing buses remove the zero >> eigenvalue/eigenvector (the "uniform translation" mode in voltage), and PV >> buses sort of push the lowest non-zero eigenvalue (related to the >> so-called >> Fiedler vector) to higher values, thus improving the condition number of >> the resulting matrix. It can be shown that a system with no PV buses >> would >> result in a condition number degrading linearly with network size. >> - The basins of attraction of the iterative methods will be >> different. This effect is in general much harder to analyze, so one has >> to >> resort to numerical experiments. >> >> >> I experimented a while back with this and I found the second effect to be >> much more dominant in practice. My set up was the following: try to solve >> cases always from a flat start, while progressively switching PV buses to >> PQ. What I found was that the loss of precision resulting from having >> slighly worse condition numbers in the Jacobian was negligible, because one >> would encounter NR non-convergence problems way before that could become >> the dominant problem. >> >> I'm attaching a test script I used for experimenting with all this. >> >> By the way, there is also another important effect to take into account: >> PV buses that are pushed over to "the other side" of their V-Q curve. In >> these buses, when you flip them to PQ, you may obtain a different voltage >> solution (it depends on your initial seed). This is because in those cases >> the solution as PV corresponds to a low-voltage branch when viewed as PQ. >> Bus 191 in case IEEE 300 is a perfect example of this; you can try it with >> my script. >> >> -- >> Jose L. Marin >> Grupo AIA >> >> >> 2016-07-27 9:13 GMT+02:00 davor sutic <[email protected]>: >> >>> Should I expect a convergent and (reasonably) accurate power flow >>> solution, when I experiment with changing the bus type PQ->PV and >>> vice versa? >>> >>> If so, is there a minimum number of each bus type required, e.g. >>> consider a system where there are only PQ buses (apart from one slack, of >>> course)? >>> >>> The data in the test cases seems sufficient for such changes, however >>> I'm worried about the stability of the system of equations. >>> >>> Thanks a lot >>> >> >> >
