Yes, Jose, MATPOWER’s power flow does handle a generator at a PQ bus as you
describe. That is, it simply treats the PG and QG as fixed injections
(equivalent to a negative load).
Ray
> On Jul 28, 2016, at 9:33 AM, Jose Luis Marín <[email protected]> wrote:
>
>
> 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 <http://www.aia.es/>
>
>
>
> 2016-07-28 15:21 GMT+02:00 davor sutic <[email protected]
> <mailto:[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]
> <mailto:[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]
> <mailto:[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
>
>
>
