Well, conceptually, no I’m afraid it doesn’t answer my question. For example,
suppose you have a system with a single slack bus and you open several lines
and create an island with more load than generation, with no slack bus. How is
it possible for a DC power flow to converge* to any meaningful answer? A set of
voltage angles that satisfies the DC power balance equations does not exist.
However, in trying some examples to verify my understanding, I see that see
that MATPOWER happily returns success = 1 for some such cases, sometimes
without Matlab even issuing any warning of a singular matrix. Some of the
voltage angles are obviously garbage (extremely large), but one may not think
to check that. So, I see a potential source for the confusion on this.
I had assumed that Matlab would complain about a singular matrix in these
cases, but it seems that maybe I need to add an explicit check to the DC power
flow to set the success flag to zero in such cases. Hmmm, wonder what’s the
most reliable inexpensive check I can do?
See below for a fun example ...
Ray
* By the way, the DC power flow is computed directly by solving a linear system
of equations, not by some iterative numerical algorithm, so “converging” isn’t
really the correct term.
Example:
mpc = loadcase('case30');
mpc.branch([15; 25; 26; 32], BR_STATUS) = 0;
r = rundcpf(mpc);
case_info(r)
Hmmm, there’s an island, but everything looks fine … generation and load in the
island-without-slack even match! Must be that case30 is already a solved DC PF
case.
mpc.gen(6, PG) = 0;
r = rundcpf(mpc);
Ok, now, no errors or singular matrix warnings, but we have voltages angles
upwards of 1e15 and load and generation in island do *NOT* match. Putting a
breakpoint in dcpf.m shows that the matrix being factored has a condition
number near 1e17 … i.e. it really is singular.
> On Mar 23, 2015, at 12:16 PM, Bijay Hughes <[email protected]> wrote:
>
> AC powerflow has convergence problem in many scenarios which we all know. The
> DC powerflow converges for the whole system even if this system has one or
> many islands; however, if a system contains one or many islands the AC
> powerflow does not converge. Does this answer your question?
>
> On Mon, Mar 23, 2015 at 11:44 PM, Ray Zimmerman <[email protected]
> <mailto:[email protected]>> wrote:
> I don’t understand approach (1). I don’t know why you say that DC power flow
> implies you don’t have to keep track of islanding. How does the AC or DC
> power flow make a difference here?
>
> Ray
>
>
> > On Mar 20, 2015, at 6:08 AM, Bijay Hughes <[email protected]
> > <mailto:[email protected]>> wrote:
> >
> > Hej all,
> >
> > I am modeling blackout in the US transmission lines system, and have two
> > approaches to do so. I do it with DC power flow, which means I don't need
> > to take care of islanding if I don't want to (although I am aware that I
> > need to take care of isolated buses for convergence reasons). I have two
> > approaches to do so: (1) do cascading failure simulation on whole system
> > each iteration, whereby one doesn't keep track of islands; (2) do cascading
> > failure simulation on the whole system to begin, see if islands are formed,
> > and run the same simulation on each of these islands, and repeat the
> > process exhaustively. In both cases, the powerflow converges as it is DC
> > flow. However, the results are not matching, and I am wondering why. Could
> > it be because of the difference in the number of slack buses? Because in my
> > approach (1) the system will only have one slack bus in each iteration,
> > however in my approach (2) the system will have multiple slack buses as the
> > matpower chooses slack buses for each island automatically, thereby my
> > system as a whole will have multiple slack buses. Is this the only reason?
> > Which approach is better, (1) or (2)?
> >
> > Best,
> >
> > BH
>
>
>
>
